Annexure ‘AAB-CD-01’
Course Title: Advance Real Analysis
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
# Course Title
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)
1 Course Objectives:
 to understand the basic concepts of real analysis and its physical properties
 to develop fundamental knowledge and understanding of the many
techniques in Real variable .
 to make the students aware of General theory of differentiation and
integration under the sign of integration, question of convergence of
series, Dirichlet’s integral, Laplace and Laplace Steiltjes transform are
employed in the theory of probability distributions. Similarly, BolzanoWeirstrass,Heine Borel theorems etc. are very much useful in Statistical
Inference .
 to apply statistical concepts to various fields of statistics to analyze and
interpret data.
2 Prerequisites:
NIL
3 Student Learning Outcomes:

The students will be able to learn various continuity of
functions.
 The students will able to acquire knowledge on convergences.
 The students will able to apply the properties of mgf and cf for
distributions.
 The students will able to define sequences of the functions.
 The course enables the students to develop the skill set to
solve the problems based on real life situation.
Course Contents / Syllabus:
4 Module I:
20%
Weightage
Monotone functions and functions of bounded variation. Real valued
functions, continuous functions, Absolute continuity of functions,
standard properties, uniform continuity, sequence of functions,
uniform convergence, power series and radius of convergence.
5 Module II:
20%
Weightage
Riemann-Stieltjes integration, standard properties, multiple integrals
and their evaluation by repeated integration, change of variable in
multiple integration. Uniform convergence in improper integrals,
differentiation under the sign of integral - Leibnitz rule, Integration
under the sign of differentiation. Dirichlet integral.
6 Module III:
30%
Weightage
Introduction to n-dimensional Euclidean space, open and closed
intervals (rectangles), compact sets, Bolzano-Weierstrass theorem,
Heine-Borel theorem. Maxima-minima of functions of several
variables, constrained maxima-minima of functions.
7 Module IV: Applications of mgf and cf for continuous
30%
distributions
Weightage
Laplace and Laplace-Steiltjes transforms. Solutitions of linear
differential.Properties of Laplace transforms, Transforms of
derivatives, Transforms of integrals, Evalualtion of integrals using
Laplace transform, convolution theorem, Applications to differential
equations, simultaneous linear equations with constant coefficient, unit
step functions and Periodic functions.
8 Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using
software in a separate Lab sessions. In addition to numerical
applications, the real life problems and situations will be assigned to
the students and they are encouraged to get a feasible solution that
could deliver meaningful and acceptable solutions by the end users.
The focus will be given to incorporate probability and related
measures to develop a risk model for various applications.
9
Assessment/ Examination Scheme:
Theory L/T
(%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop
down)
Weightage
(%)
70%
End Term
Examination
Mid- Project Viva Attendance
Term
Exam
10%
10%
5%
5%
70%
Text & References:






Rudin, Walter (1976). Principles of Mathematical Analysis, McGraw Hill.
Apostol, T. M. (1985). Mathematical Analysis, Narosa, Indian Ed.
Narayan, S., (2010). Elements of Real Analysis, S. Chand and Sons.
Miller, K. S. (1957). Advanced Real Calculus, Harper, New York
Courant, R. and John, F. (1965). Introduction to Calculus and Analysis, Wiley
Bartle, R.G. (1976): Elements of Real Analysis, John Wiley & Sons.
Annexure ‘AAB-CD-01’
Course Title: PROBABILITY THEORY
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
 The objective of the course is to develop knowledge of the
fundamentals of the probability theory for determining the risk and
assessing the various problems based on it.
 The application of this theory in various decision making problems
especially under uncertainties.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)

The students will be able to distinguish between probability models
appropriate to different chance events and calculate probability
according to these methods.
 The students will learn to get the solution of the problems based on
probability space and limit theorems.
 The students will learn to get the solution of the problems based on
random variables and distribution functions.
 The students will learn to get the solution of the problems based on
mgf and cf for discrete and continuous distributions.
 The course enables the students to develop the skill set to apply
probability theory in real life problems.
Course Contents / Syllabus:
4 Module I: Probability Space and Limit Theorems
5
Probability Space:
 Definition of probability
 Some simple properties
 Discrete probability space
 Induced probability space
 Other measures-Complements and problems
Limit Theorems:
 Introduction
 Modes of conversion
 Weak law of large numbers
 Strong law of large numbers
 Limiting moment generating functions
 Central limit theorem
Module II: Random variables and Distribution Functions









Random variables
Functions of Random variables
Probability density function
Probability mass function
Distribution function and its properties
Representation of distribution as a mixture of distributions
Compound, truncated and mixture distributions
Decomposition of distribution functions
Distribution functions of vector random variables
20%
Weightage
20%
Weightage
6
 Correspondence theorem
 Complements and problems
Module III: Applications of mgf and cf for discrete distributions
30%
Weightage





7
Mathematical expectation and moments
Probability generating function (PGF)
Moment generating function (MGF)
Characteristic function (CF): Definition and simple properties
Examples of discrete distributions: Degenerate, Uniform, Bernaulli,
Binomial, Poisson, Geometric, Negative Binomial and Hyper
geometric distribution,
 Convergence of distribution function.
 Complements and problems
Module IV: Applications of mgf and cf for continuous distributions
30%
Weightage



8
MGF and CF for continuous r.v.
Inversion theorem
Examples of continuous distributions: Uniform, Normal,
Exponential, Gamma, Beta, Weibull, Pareto, Laplace, Lognormal,
Logistic and Log-Logistic distribution.
 Bochner’s theorem
 Complements and problems
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
probability and related measures to develop a risk model for various
applications.
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:
1. Bhat, B. R (1981): Modern Probability Theory, Wiley Eastern Ltd., New Delhi.
2. Rohatgi, V. K. (1988): An Introduction to Probability and Mathematical Statistics, Wiley,
Eastern Limited.
Annexure ‘AAB-CD-01’
Course Title: STATISTICAL METHODS
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
 The main objective of the course is to provide the detailed
knowledge of the characterization of all the useful discrete,
absolutely continuous and singular distributions.
 Interrelations of various Statistical models producing different
families require further investigations.
 To develop the knowledge of order statistics and theory and
applications of non-parametric methods.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)

The students will learn about the concepts and applications of order
statistics to handle the real life problems.
 The students will able to learn how to solve the problems by using
non-parametric methods.
 The students will learn about the various non-parametric tests.
 The students will able to distinguish between one sample and two
sample non-parametric tests.
Course Contents / Syllabus:
4 Module I: Order Statistics
20%
Weightage






5
Definition and concept of Order Statistics
Discrete & continuous Order Statistics
Joint and marginal distribution of order statistics
Distribution of range
Distribution of censored sample
Numeric examples and applications based on continuous
distributions.
 Complement and problems
Module II: Interval estimation and U-Statistics
6
 Confidence intervals for distribution
 Quantiles
 Tolerance limits for distributions
 Asymptotic distribution of function of sample moments
 U-Statistics,
 Transformation and Variance stabilizing results.
 Complement and problems
Module III: Non-parametric tests-I (based on location)
20%
Weightage
30%
Weightage

7
One sample problem: Sign test, signed rank test, KolmogrovSmirnov test, Test of independence (run test).
 Two sample problem: Wilcoxon-Mann-Whitney test, Median test,
Kolmogrov-Smirnov test, run test.
 Complement and problems
Module IV: Non-parametric tests-II (based on scale)
30%
Weightage
8
9
 Ansari-Bradely test
 Mood test
 Kendall’s Tau test
 Test of randomness
 Consistency of tests and ARE
 Complements and problems
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the applications of order statistics and non-parametric methods for solving the
real life problems and cases.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:
1. Gibbons, J.D. (1971): Non-parametric Statistical Inference, Mc Graw Hill Inc.
2. Hogg, R.V. & Raise, A.T. (1978): Introduction to mathematical satsitics, Macmillan Pub. Co.
Inc.
Annexure ‘AAB-CD-01’
Course Title: Linear algebra and application
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
The motivation of introducing Linear Algebra course in Statistics is mainly to
evolve the basics of Algebra. The main objective to introduce this course is to
solve various problems by computing the inverse of a matrix, the Unique
Moore and Penrose generalized inverse methods.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
4
Feedback
Rating
(on scale of
6 points)

The students will learn about the basic concepts of vector space,
linear transformation.
 The students will able to compute the rank of the given matrix,
eignvalues.
 The students will able to learn how to calculate Generalized Inverses
of matrices.
 The students will learn about the quadratic forms, quadratic and
singular value decomposition.
Course Contents / Syllabus:
4 Module I:
5
Examples of vector spaces, vector spaces and subspace, independence in
vector spaces, existence of a Basis, the row and column spaces of a matrix,
sum and intersection of subspaces.
Module II:
6
Linear Transformations and Matrices, Kernel, Image, and Isomorphism,
change of bases, Similarity, Rank and Nullity.
Module III:
7
Inner Product spaces, orthonormal sets and the Gram-Schmidt Process, the
Method of Least Squares.
Basic theory of Eigenvectors and Eigenvalues, algebraic and geometric
multiplicity of eigen value, diagonalization of matrices, application to system
of linear differential equations .Factorization of Matrices
Module IV:
8
Generalized Inverses of matrices, Moore-Penrose generalized inverse. Real
quadratic forms, reduction and classification of quadratic forms, index and
signature, triangular reduction of a reduction of a pair of forms, Quadractic
and singular value decomposition, extrema of quadratic forms. Jordan
canonical form, vector and matrix decomposition
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:







Biswas, S. (1997): A Text Book of Matrix Algebra, 2nd Edition, New Age International Publishers.
Golub, G.H. and Van Loan, C.F.(1989): Matrix Computations, 2nd edition, John Hopkins University Press,
Baltimore-London.
Nashed, M.(1976): Generalized Inverses and Applications, Academic Press, New York.
Rao, C.R.(1973): Linear Statistical Inferences and its Applications, 2nd edition, John Wiley and Sons.
Robinson, D.J.S. (1991): A Course in Linear Algebra with Applications, World Scientific, Singapore.
Searle, S.R.(1982): Matrix Algebra useful for Statistics, John Wiley and Sons.
Strang, G.(1980): Linear Algebra and its Application, 2nd edition, Academic Press, London-New York.
Annexure ‘AAB-CD-01’
Course Title: Optimization Techniques and
Applications
L
T
Course Code: to be decided later
Credit Units: 4
Level: PG
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
The objective of this course is to enhance the applications of optimization
techniques in engineering system and real life situations as well. The main
aim of this course is to present different methods to solve the constrained
optimization problems by using linear programming, integer linear
programming. In addition the use of optimization techniques is also explained
for network planning and scheduling.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)

The students will learn about the formulation of the given real life
problem as mathematical programming problem.
 The students will acquire the knowledge for solving linear
programming problems and will able to interpret the results.
 The students will able to minimize the transportation costs for the
transportation problems.
 The students will able to plan and schedule the network analysis.
Course Contents / Syllabus:
4 Module I:
Linear Programming Problems (LPP)
Introduction to LPPs, Solution of LPPs: Graphical Method & Simplex
Method, Use of Artificial Variables in simplex method: Charnes’ Big M
method and Two Phase Method, Duality in LPPs, Dual Simplex Method .
5 Module II:
20%
Weightage
20%
Weightage
Transportation Problems (TP)
Introduction to Transportation Problem, TP as a case of LPP, Methods to
obtain initial basic feasible solution to a TP: North West Corner Rule, Matrix
Minima Method, Vogel’s Approximation Method, Solution of the TP by
MODI method, Degeneracy in TPs, Unbalanced transportation problems and
their solutions.
Assignment Problems (AP): Introduction to APs, AP as a complete
degenerate form of TP, Hungarian Method for solving APs, Unbalanced
Assignment problems and their solutions, APs with restrictions.
6
Module III:
30%
Weightage
Integer Linear Programming Problems
Integer Linear Programming Problems, Mixed Integer Linear Programming
Problems, Cutting Plane Method, Branch and Bound Method.
7
Module IV:
Project scheduling
Network representation of a Project Rules for construction of a Network. Use
of Dummy activity. The critical Path method (CPM) for constructing the
time schedule for the project. Float (or shack) of an activity and event.
Programme Evolution and Review Technique (PERT). Probability
considerations in PERT. Probability of meeting the scheduled time. PERT
Calculation, Distinctions between CPM and PERT.
30%
Weightage
8
Pedagogy for Course Delivery:
9
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:






Hadley, G., “Linear Programming,”, Addison-Wesley, Mass.
Taha, H.A. “Operations Research – An Introduction”, Macmillian
F.S. Hiller, , G.J. Lieberman, ” Introduction to Operations Research”, Holden-Day
Harvey M. Wagner, “Principles of Operations Rsearch with Applications to Managerial
Decisions”, Prentice Hall of India Pvt. Ltd.
K. Swarup, P. K. Gupta and Man Mohan, “Operations Research”, Sultan Chand & Sons, New
Delhi.
Panneerselvam, “Operations Research” 2nd edition, PHI Pvt. Ltd.
Annexure ‘AAB-CD-01’
Course Title: Advanced Statistical Inference – I
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
In Statistics population parameters describe the characteristics under study.
These parameters need to be estimated on the basis of collected data called
sample. The purpose of estimation theory is to arrive at an estimator that
exhibits optimality. The estimator takes observed data as an input and
produces an estimate of the parameters. This course will make a student learn
the various properties of a good estimator as well as techniques to develop
such estimators from both classical and Bayesian point of view.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)

The students will able to learn about the various requirements to be a
good estimator.
 The students will able to emphasize the statistical thinking.
 The students will able to use technology by using various properties
of statistical inference.
 The students will able to distinguish the common elements of
inference procedures.
Course Contents / Syllabus:
4 Module I:
20%
Weightage
Criterion of a good estimator- unbiasedness, consistency, efficiency and
sufficiency. Minimal sufficient statistics. Exponential and Pitman family of
distributions. Complete sufficient statistic, Rav-Blackwell theorem,
Lehmann-Scheffe theorem, Cramer-Rao lower bound approach to obtain
minimum variance unbiased estimator (mvue).
5
Module II:
20%
Weightage
Maximum likelihood estimator (mle), its small and large sample properties,
CAN & BAN estimators, Most Powerful (MP), Uniformly Most Powerful
(UMP) and Uniformly Most Powerful Unbiased (UMPU) tests. UMP tests for
monotone likelihood ratio (MLR) family of distributions.
6
Module III:
30%
Weightage
Likelihood ratio test (LRT) with its asymptotic distribution, Similar tests with
Neyman structure, Ancillary statistic and Basu’s theorem. Construction of
similar and UMPU tests through Neyman structure.
7
Module IV:
Interval estimation, confidence level, construction of confidence intervals
using pivots, shortest expected length confidence interval, uniformly most
accurate one sided confidence interval and its relation to UMP test for one
sided null against one sided alternative hypothesis.
30%
Weightage
8
9
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:
1. Lehmann, E.L. (1983): Theory of Point Estimation, Wiley.
2. Lehmann, E.L. (1986): Testing Statistical Hypothesis, 2 nd Ed., Wiley.
3. Rao, C.R. (1973): Linear Statistical Inference and its Applications, Wiley.
4. Rohatgi, V.K. (1976): An introduction to Probability Theory and Mathematical Statistics, Wiley.
Annexure ‘AAB-CD-01’
Course Title: Advanced Sample Theory
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
This course is designed to provide an overview of the theory and applications
of various sampling procedures in survey research methods. The objective of
this course is to emphasize the knowledge on survey process and the field of
survey research.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)

The students will able to learn various techniques used in sampling
practices.
 The students will learn how to interpret the descriptive statistics for
the given data.
 The students will able to conceptualize, conduct, interpret the
statistical analyses for the different population.
Course Contents / Syllabus:
4 Module I:
Estimation of population mean, total and proportion in SRS and Stratified
sampling. Estimation of gain due to stratification. Ratio and regression
methods of estimation. Unbiased ratio type estimators. Optimality of ratio
estimate .Separate and combined ratio and regression estimates in stratified
sampling and their comparison.
5 Module II:
20%
Weightage
20%
Weightage
Cluster sampling: Estimation of population mean and their variances based on
cluster of equal and unequal sizes. Variances in terms of intra-class
correlation coefficient. Determination of optimum cluster size.
Varying probability sampling: Probability proportional to size (pps) sampling
with and without replacement and related estimators of finite population
mean.
6
Module III:
Two stage sampling: Estimation of population total and mean with equal and
unequal first stage units. Variances and their estimation. Optimum sampling
and sub-sampling fractions (for equal fsu’s only).Selection of fsu’s with
varying probabilities and with replacement
7 Module IV:
Double Sampling: Need for double sampling. Double sampling for ratio and
regression method of estimation. Double sampling for stratification. Sampling
on two occasions.
Sources of errors in surveys: Sampling and non-sampling errors. Various
types of non –sampling errors and their sources .Estimation of mean and
proportion in the presence of non-response. Optimum sampling fraction
among non–respondents. Interpenetrating samples. Randomized response
technique.
8
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
30%
Weightage
30%
Weightage
9
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:
1. Cockran, W.G., (1977): Sampling Techniques, 3rd edition, John Wiley.
2. Des Raj and Chandak (1998): Sampling theory, Narosa.
3. Murthy, M.N. (1977): Sampling theory and methods. Statistical Publishing Society, Calcutta.
4. Sukhatme et al. (1984): Sampling theory of surveys with applications, Lowa state university press and
ISAS.
5. Singh, D. and Chaudary, F.S. (1986): Theory and analysis of sample survey designs. New age
international publishers
Annexure ‘AAB-CD-01’
Course Title: Linear Model and Regression Analysis
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
This course focuses on building a greater understanding, theoretical
underpinning, and tools for applying the linear regression model and its
generalizations. With a practical focus, it explores the workings of multiple
regression and problems that arise in applying it, as well as going deeper
into the theory of inference underlying regression and most other statistical
methods. The course also covers new classes of models for binary and count
data, emphasizing the need to fit appropriate models to the underlying
processes generating the data being explained.
2
Prerequisites:
NIL
Student Learning Outcomes:
3



SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)
The students will learn the linear estimation and able to identify the
best linear unbiased estimator among various estimators.
The students will able to learn various tests of statistical
hypotheses.
The students will know the differences between linear and
nonlinear models.
Course Contents / Syllabus:
4 Module I:
5
Linear Estimation: Gauss-Markov linear Models, Estimable functions, Error
and Estimation Spaces, Best Linear Unbiased Estimator (BLUE), Least
square estimator, Normal equations, Gauss-Markov theorem, generalized
inverse of matrix and solution of Normal equations, variance and covariance
of Least square estimators.
Module II:
6
Test of Linear Hypothesis: One way and two way classifications. Fixed,
random and mixed effect models (two way classifications only), variance
components
Module III:
20%
Weightage
20%
Weightage
30%
Weightage
Linear Regression: Bivariate, Multiple and polynomials regression and use
of orthogonal polynomials. Residuals and their plots as tests for departure
from assumptions of fitness of the model normality, homogeneity of
variance and detection of outlines. Remedies.
7
Module IV:
8
Non Linear Models: Multi-collinearity, Ridge regression and principal
components regression, subset selection of explanatory variables, Mallon’s
Cp Statistics.
Pedagogy for Course Delivery:
30%
Weightage
9
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:






Goon, A.M., Gupta, M.K. and Dasgupta, B. (1987): An Outline of Statistical Theory, Vol. 2, The World
Press Pvt. Ltd. Culcutta.
Rao, C.R. (1973): Introduction to Statistical Infererence and its Applications, Wiley Eastern.
Graybill, F.A. (1961): An introduction to linear Statistical Models, Vol. 1, McGraw Hill Book Co. Inc.
Draper, N.R. and Smith, H (1998): Applied regression Analysis, 3 rd Ed. Wiley.
Weisberg, S. (1985): Applied linear regression, Wiley.
Cook, R.D. and Weisberg, S. (1982): Residual and Inference in regression, Chapman & Hall.
Annexure ‘AAB-CD-01’
Course Title: Experimental Design
L
T
P/
S
SW/F
W
TOTAL
CREDIT
Course Code: to be decided later
Credit Units: 4
Level: PG
3
1
#
Course Title
1
Course Objectives:
The course objective is to learn how to plan, design and conduct
experiments efficiently and effectively, and analyze the resulting data to
obtain objective conclusions. Both design and statistical analysis issues are
discussed. Opportunities to use the principles taught in the course arise in all
phases of engineering work, including new product design and development,
process development, and manufacturing process improvement.
Applications from various fields of engineering (including chemical,
mechanical, electrical, materials science, industrial, etc.) will be illustrated
throughout the course. Computer software packages (Design-Expert,
Minitab) to implement the methods presented will be illustrated extensively,
and you will have opportunities to use it for
homework assignments and the term project.
2
Prerequisites:
NIL
Student Learning Outcomes:
3



0
UNITS
4
Weightage
(%)
The students will able to learn about basic principles of design of
experiments.
The students will able to do various experimental design for the
given data.
The students will learn the analysis of series experiments.
Course Contents / Syllabus:
4 Module I:
20%
Weightage
Analysis of Basic Design: Asymptotic relative efficiency, Missing plot
technique, Analysis of covariance for CRD and RBD.
5
Module II:
20%
Weightage
Factorial Experiments: 2n, 32 and 33 systems only. Complete and Partial
Confounding. Factorial Replication in 2n systems.
6
Module III:
30%
Weightage
Incomplete Block Design: Balanced Incomplete Block Design, Simple
Lattice Design, Split-plot Design, Strip-plot Design.
7
8
9
Module IV:
30%
Weightage
Application Areas: Response surface areas. First and second order designs.
Model validation and use of transformation. Analysis of series experiments,
groups of experiment in time and space.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:
1. Das, M.N. and Giri, N.C. (1979): Design and Analysis of Experiment, Wiley Eastern.
2. Giro (1986): Analysis of Variance, South Asian Publishers.
3. Day, Alok (1986): theory of Block Design, Wiley Eastern.
Annexure ‘AAB-CD-01’
Course Title: Mathematical Demography
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Mathematical Demography deals with the Population Analysis by building
Mathematical or Statistical models relating the growth of population by
investigating its components like Fertility, Mortality and Migration and
builds up Population Projection techniques. The applicability of the subject
is very wide in National planning is highly Significant. A student will get
insight as to mechanism that determines Population growth which is very
useful in National Planning as well as in Actuarial Science in solving
Insurance problems.
2
Prerequisites:
NIL
Student Learning Outcomes:
3



SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)
The students will able to lean the basic concepts of mathematical
demography.
The students will able to construct the life table.
The students will learn about the risk theory.
Course Contents / Syllabus:
4 Module I:
Sources of Demographic data, Coverage and content errors in demographic
data, Chandrasekharan—Deming formula to check completeness of
registration data, adjustment of age data- use of Whipple, Myer and UN
indices. population transition theory.
5 Module II:
20%
Weightage
20%
Weightage
Measures of mortality, description of life table, construction of complete and
abridged life tables, maximum likelihood, MVU and CAN estimators of life
table parameters. Model life table, Measures of fertility, Indices of fertility
measures, Relationship between CBR, GFR and TFR, Mathematical Models
on fertility
6
Module III:
30%
Weightage
Population growth indices: measurement of population growth, logistic
model, methods of fitting logistic curves, Stable population analysis,
Population projection techniques, Frejka’s component method,
Representation of component method by the use of Leslie matrix.
7
Module IV:
Internal migration and its measurement, migration models, concept of
international Migration, Nuptiality and its measurements.
Competing risk Theory: Measurement of competing risks, Inter-relations of
the death probabilities, Estimation of crude, net and partial crude
probabilities of death.
8
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
30%
Weightage
9
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:






Samuel Preston, Patrick Heuveline, Michel Guillot (2000) Demography: Measuring and Modeling
Population Processes, Wiley-Blackwel.
Biswas, S. (1988): Stochastic Processes in Demography and Applications, Wiley Eastern Ltd.
Chiang, C.L. (1968): Introduction to Stochastic Processes in Bio statistics, John Wiley.
Keyfitz, N. (1971): Applied Mathematical Demography, Springer Verlag.
Spiegelman, M. (1969): Introduction to Demographic Analysis, Harvard University Press.
Kumar, R. (1986): Technical Demography, Wiley Eastern Ltd.
Annexure ‘AAB-CD-01’
Course Title: Advanced Biostatistics
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
To acquaint Public Health master and doctoral student with methods for
analyzing correlated data without requiring a high level of mathematical
sophistication. The course should we helpful in the analysis of research data
and doctoral dissertation projects.
Prerequisites:
NIL
Student Learning Outcomes:
2
3


SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage
(%)
The students will able to use the applications of statistics in clinical
data.
The students will able to interpret the results of the given data with
the help of different mathematical models.
Course Contents / Syllabus:
4 Module I:
5
Parametric methods for comparing two survival distributions viz. L.R test,
Cox’s F-test. P-value, Analysis of Epidemiologic and Clinical Data:
Studying association between a disease and a characteristic: (a) Types of
studies in Epidemiology and Clinical Research (i) Prospective study (ii)
Retrospective study (iii) Cross-sectional data, (b) Dichotomous Response
and Dichotomous Risk Factor: 2X2 Tables (c) Expressing relationship
between a risk factor and a disease (d) Inference for relative risk and odds
ratio for 2X2 table, Sensitivity, specificity and predictivities, Cox
proportional hazard model.
Module II:
6
Bivariate normal dependent risk model. Conditional death density functions.
Stochastic epidemic models: Simple and general epidemic models (by use of
random variable technique). Basic biological concepts in genetics, Mendels
law, Hardy- Weinberg equilibirium, random mating, distribution of allele
frequency (dominant/co-dominant cases), Approach to equilibirium
Module III:
20%
Weightage
20%
Weightage
30%
Weightage
Analysis of Epidemiologic and Clinical Data: Studying association between
a disease and a characteristic: (a) Types of studies in Epidemiology and
Clinical Research (i) Prospective study (ii) Retrospective study (iii) Crosssectional data, (b) Dichotomous Response and Dichotomous Risk Factor:
2X2 Tables (c) Expressing relationship between a risk factor and a disease
(d) Inference for relative risk and odds ratio for 2X2 table, Sensitivity,
specificity and predictivities,
7
Module IV:
8
for X-linked genes, natural selection, mutation, genetic drift, equilibirium
when both natural
selection and mutation are operative, detection and estimation of linkage in
heredity. Planning and design of clinical trials, Phase I, II, and III trials.
Consideration in planning a
clinical trial, designs for comparative trials. Sample size determination in
fixed sample designs.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
30%
Weightage
9
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:
 Collett, D. (2003): Modelling survival Data in Medical Research, Chapman & Hall/CRC.
 Cox, D.R. and Oakes, D. (1984). Analysis of Survival Data, Chapman Hall.
 Indrayan, A. (2008). Medical Biostatistics, Second Edition, Chapman & Hall/CRC.
 Lee, Elisa, T. (1992). Statistical Methods for Survival Data Analysis, John Wiley & Sons
 Ewens, W.J. and Grant, G.R. (2001). Statistical methods in Bio informatics: An introduction, Springer.
 Friedman, L.M., Furburg, C. and DeMets, D.L. (1998). Fundamentals of Clinical Trials, Springer Verlag.
Gross, A. J. and Clark V. A. (1975). Survival Distribution: Reliability Applications in Biomedical Sciences,
John Wiley & Sons.
Annexure ‘AAB-CD-01’
Course Title: Advanced Statistical Inference – II
L
T
P/
S
SW/F
W
TOTAL
CREDIT
Course Code: to be decided later
Credit Units: 4
Level: PG
3
1
#
Course Title
1
Course Objectives:
In Statistics population parameters describe the characteristics under study.
These parameters need to be estimated on the basis of collected data called
sample. The purpose of estimation theory is to arrive at an estimator that
exhibits optimality. The estimator takes observed data as an input and
produces an estimate of the parameters. This course will make a student
learn the various properties of a good estimator as well as techniques to
develop such estimators from both classical and Bayesian point of view.
2
Prerequisites:
NIL
Student Learning Outcomes:
3



0
UNITS
4
Weightage
(%)
The students will able to emphasize the statistical thinking in
decision theory.
The students will able to use technology by using various properties
of statistical inference.
The students will able to distinguish the common elements of
inference procedures.
Course Contents / Syllabus:
4 Module I:
20%
Weightage
5
Statistical decision problem: Decision problem and 2-person game, nonrandonized, mixed and randomized decision rules, loss function, risk
function, admissibility, Bayes rules, minimax rules, least favourable
distributions, complete class and minimal complete class.
Module II:
6
Decision problem for finite parameter space, convex loss function.
Admissible Bayes & minimax estimators, Test of simple hypothesis against
a simple alternative from decision theoretic vew point..
Module III:
7
Bayes theorem and computation of posterior distribution, Bayesian point
estimation as a prediction problem from posterior distribution, Bayes
estimators for (i) absolute loss function (ii) squared loss function and (iii) 01 loss function, Evaluation of estimates in terms of the posterior risk.
Module IV:
20%
Weightage
30%
Weightage
30%
Weightage
Bayesian interval estimation, Bayesian testing of hypothesis, Bayes
factor for various types of testing hypothesis problem depending
upon whether the null hypothesis and the alternative hypothesis are
simple or composite, Bayesian prediction problem.
8
9
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:




Farguson, T.S. (1967), Mathematical Statistics Academic.
Goon, A.M., Gupta M.K. and Dasgupta, B. (1973): An Outline of Statistical Theory, Vol.2, World Press.
Berger, J.O.: Statistical Decision theory and Bayesian Analysis, Springer-Verlag
Sinha, S.K. (1998): Bayesian Estimation, New Age International
Annexure ‘AAB-CD-01’
Course Title: Multivariate Analysis
L
T
P/
S
SW/F
W
TOTAL
CREDIT
Course Code: to be decided later
Credit Units: 4
Level: PG
3
1
#
Course Title
1
Course Objectives:
Multivariate analysis is the analysis of observations on several correlated
random variables for a number of individuals in one or more samples
simultaneously, this analysis, has been used in almost all scientific studies.
For example, the data may be the nutritional anthropometrical measurements
like height, weight, arm circumference, chest circumference, etc. taken from
randomly selected students to assess their nutritional studies. Since here we
are considering more than one variable this is called multivariate analysis.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
0
Feedback
Rating
(on scale of
6 points)

The students will learn various statistical techniques for
multivariate data.
 The students will able to do analysis by using different procedures
for multivariate data.
Course Contents / Syllabus:
4 Module I:
20%
Weightage
Singular and non-singular multivariate normal distributions, Characteristic
function of N p (  , ) Maximum likelihood estimators of  and  in
N p (  , ) and their independence.
5
Module II:
6
Wishart distribution: Definition and its distribution, properties and
characteristic function. Generalized variance. Testing of sets of variates and
equality of covariance.
Estimation of multiple and partial correlation coefficients and their null
distribution, Test of hypothesis on multiple and partial correlation
coefficients.
Module III:
7
Hotelling’s 𝑇 2 : Definition, distribution and its optimum properties.
Application in tests on mean vector for one and more multivariate normal
population and also on equality of the components of a mean vector of a
multivariate normal population. Distribution of
Mahalanobis’s 𝐷 2 .
Discriminate analysis: Classification of observations into one or two or more
groups. Estimation of the misclassification probabilities. Test associated
with discriminate functions.
Module IV:
Principal component, canonical variate and canonical
Definition, use, estimation and computation. Cluster analysis.
8
9
UNITS
4
20%
Weightage
correlation:
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
30%
Weightage
30%
Weightage
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:
 Anderson, T.W. (1984): An introduction to multivariate statistical analysis. John Wiley.
 Giri, N.C. (1977): Multivariate statistical inference. Academic Press.
 Singh, B.M. (2002): Multivariate statistical analysis. South Asian Publishers.
.
Annexure ‘AAB-CD-01’
Course Title: Stochastic Processes and Applications
L
T
P/
S
SW/F
W
TOTAL
CREDIT
Course Code: to be decided later
Credit Units: 3
Level: PG
2
1
#
Course Title
1
Course Objectives:
Stochastic process, or sometimes random process is a collection of random
variables; this is often used to represent the evolution of some random value,
or system, over time. Familiar examples of processes modeled as stochastic
time series include stock market and exchange rate fluctuations, signals such
as speech, audio and video, medical data
such
as
a
patient's EKG, EEG, blood pressure or temperature, and random movement
such as Brownian motion or random walks.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
Weightage
(%)
 The students will able to learn the basics of stochastic processes.
 The students will learn about the Renewal theory.
Course Contents / Syllabus:
4 Module I:
5
Introduction to Stochastic Processes (sp’s); classification of sp’s according
to state space and time domain. Countable state Markov chains (MC’s),
Chapman-Kolmogorov equations, calculation of n-step transition
probabilities and their limits. Stationary distribution, classification of states,
transient MC. Random walk and gambler’s ruin problem. Applications of
stochastic processes. Stationarity of stochastic processes, autocorrelation,
power spectral density function, power of a process.
Module II:
6
Discrete state space continuous time MC, Kolmogorov- Feller differential
equations, Poisson process, birth and death process
Module III:
7
Renewal theory: Elementary renewal theorem and applications. Statement
and uses of key renewal theorem, study of residual lifetime process.
Branching process: Galton-Watson branching process, probability of
ultimate extinction, distribution of population size.
Module IV:
8
9
0
UNITS
3
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
Martingale in discrete time, inequality, convergence and smoothing
properties, Queueing processes, application to queues –M/M/1 and M/M/C
models.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
NA
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:












Mehdi, J. (1994): Stochastic Processes, Wiley Eastern 2 nd Ed.
Groos, Da Harris, C.M. (1985): Fundamental of Queuing Theory, Wiley.
Biswas, S. (1995): Applied Stochastic Processes, Wiley.
Adke, S.R. and Manjunath, S.M. (1984): An Introduction to Finite Markov Processes, Wiley Estern.
Bhat, B.R. (2000) : Stochastic Models: Analysis and Applications, New Age International, India. Chapter
13 (13.1-13.3).
Cinlar, E. (1975) : Introduction to Stochastic Processes, Prentice Hall.
Feller, W. (1968) : Introduction to Probability Theory and its Applications, Vol.1, Wiley Eastern.
Harris, T.E. (1963): The Theory of Branching Processes, Springer – Verlag.
Hoel, P.G., Port S.C. and Stone, C.J. (1972) : Introduction to Stochastic Processes, Houghton Miffin & Co.
Jagers, P. (1974) : Branching Processes with Biological Applications, Wiley.
Karlin, S. and Taylor, H.M. (1975) : A First Course in Stochastic Processes, Vol.1, Academic Press.
Parzen, E. (1962): Stochastic Processes, Holden – Day.
Annexure ‘AAB-CD-01’
Course Title: Statistical Quality Control
Course Code: to be decided later
Credit Units: 3
Level: PG
L
T
2
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
Quality Control is a comprehensive course in QC terminology, practices,
statistics, and troubleshooting for the clinical laboratory. Designed for those
who have little or no experience with quality control but need a firm
grounding, this course will help all students quickly and easily identify and
correct errors in quality control procedures. Concepts covered include:
running assayed and unassayed controls, specificity, sensitivity, Westgard
rules, Levey-Jennings charts, Youden plots, and CUSUM calculations.
MediaLab also offers an "Introduction to Quality Control" course to
complement the more detailed and thorough presentation in this course.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
3
Weightage
(%)

The students will learn the basic concepts of quality control for
industrial purposes.
 The students will able to construct various control charts for
monitoring the process control.
Course Contents / Syllabus:
4 Module I:
5
Basic concept of process, monitoring and control process capability and
process optimization, General theory and review of control charts for attribute
and variable data; OC and A. R. L. of control charts, moving average and
exponentially distributed moving average charts. Cu-Sum charts, using Vmarks and decision interval.
Module II:
6
Acceptance sampling plans for attribute inspection; single, double sampling
plans and their properties, (ATI, AOQ, ASN,--------Module III:
7
Capability indices Cp, Cpk, and Cpm; estimation, confidence intervals and
tests of hypothesis relating to capability for normally distributed
characteristics.
Module IV:
8
Use of Design of Experiments in SPC; factorial experiments construction of
such designs and analysis of data.
Pedagogy for Course Delivery:
9
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
NA
End Term
Examination
70%
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:
1. Montgomery, D. C. (1985): Introduction of Statistical Quality Control, Wiley.
2. Montgomery, D. C. (1985): Design and Analysis of Experiments; Wiley.
3. Ott, E. R. (1975): Process Quality Control. McGraw Hill.
Annexure ‘AAB-CD-01’
Course Title: Survival Analysis
Course Code: to be decided later
Credit Units: 3
Level: PG
L
T
2
1
P/
S
#
Course Title
1
Course Objectives:
Survival Analysis is a collection of methods for the analysis of data that
involve the time to occurrence of some event, and more generally, to
multiple durations between occurrences of different events or a repeatable
(recurrent) event. From their extensive use over decades in studies of
survival times in clinical and health related studies and failures times in
industrial engineering (e.g., reliability studies), these methods have evolved
to special applications in several other fields, including demography (e.g.,
analyses of time intervals between successive child births), sociology (e.g.,
studies of recidivism, duration of marriages), and labor economics
(e.g., analysis of spells of unemployment, duration of strikes).
2
Prerequisites:
NIL
Student Learning Outcomes:
3
SW/F
W
0
TOTAL
CREDIT
UNITS
3
Weightage
(%)

The students will able to learn the basic concepts of survival
analysis.
 The students will able to study different life distributions for
research purposes.
 The students will learn how to estimate the survival function.
Course Contents / Syllabus:
4 Module I:
5
Concepts of Type-I (time), Type-II (order) and random censoring likelihood
in these cases. Life
distributions, exponential, gamma, Weibull, lognormal, Pareto, linear failure
rate. Inference for
exponential, gamma, Weibull distributions under censoring.
Module II:
6
Failure rate, mean residual life and their elementary properties. Ageing
classes and their properties,bathtub failure rate.
Module III:
7
Estimation of survival function – Actuarial estimator, Kaplan –Meier
estimator, Tests of exponentiality against non-parametric classes: Total time
on Test, Deshpande Test.
Module IV:
Two sample problem : Gehan test, Log rank test. Mantel-Haenszel test,
Cox’s proportional hazards model, competing risks model.
8
Pedagogy for Course Delivery:
9
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:






Cox, D.R. and Oakes, D. : Analysis of Survival Data, Chapters 1, 2, 3, 4.
Crowder Martin, J. (2001): Classical Competing Risks, Chapman & Hall, CRC, London.
Gross, A.J. & Clark, V.A.: Survival Distributions-Reliability Applications in Biomedical Sciences,
Chapters 3,4.
Elandt-Johnson, R.E. and John, N.L.: Survival Models and Data Analysis, John Wiley
and Sons.
Miller, R.G. (1981): Survival Analysis, Chapters 1-4.
Kalbfleisch, J.D. and Prentice, R.L. (1980): The Statistical Analysis of Failure Time Data,
John Wiley.
Annexure ‘AAB-CD-01’
Course Title: Theory of Econometrics
Course Code: to be decided later
Credit Units: 3
Level: PG
L
T
2
1
P/
S
#
Course Title
1
Course Objectives:
A significant development of Mathematical Economics is the increased
application of probabilistic tools and Statistical techniques known as
“Econometrics”.
A reasonable understanding of econometric principles is indispensable for
further studies in economics. This course is aimed at introducing students to
the most fundamental aspects of both mathematical economics and
econometrics. The objective of this paper is to apply both deterministic as
well as Stochastic models for the purpose of Planning. The techniques of
estimation in Econometrics like’ two or three stage Least squares’ are
entirely non traditional than that of classical estimation in Statistics.With the
knowledge of the contents of this paper students will acquire how Modern
Statistics answers Economic problems.
2
Prerequisites:
NIL
Student Learning Outcomes:
3


SW/F
W
0
TOTAL
CREDIT
UNITS
3
Feedback
Rating
(on scale of
6 points)
The students will able to apply the basic concepts of economics for
interpreting the results of the given data.
The students will able to acquire knowledge on Market
Equilibrium.
Course Contents / Syllabus:
4 Module I:
5
Introduction to Mathematical Economics
Mathematical Economics: Meaning and Importance- Mathematical
Representation of Economic Models- Economic functions: Demand
function, Supply function, Utility function, Consumption function,
Production function, Cost function, Revenue function, Profit function,
Saving function, Investment function Marginal Concepts: Marginal utility,
Marginal propensity to Consume, Marginal propensity to Save, Marginal
product, Marginal Cost, Marginal Revenue, Marginal Rate of Substitution,
Marginal Rate of Technical Substitution Relationship between Average
Revenue and Marginal Revenue- Relationship between Average Cost and
Marginal Cost - Elasticity: Demand elasticity, Supply elasticity, Price
elasticity, Income elasticity, Cross elasticity- Engel function.
Module II:
6
Constraint Optimisation, Production Function and Linear
Programming
Constraint optimisation Methods: Substitution and Lagrange MethodsEconomic applications: Utility Maximisation, Cost Minimisation, Profit
Maximisation. Production Functions: Linear, Homogeneous, and Fixed
production Functions- Cobb Douglas production function- Linear
programming: Meaning, Formulation and Graphic Solution.
Module III:
Market Equilibrium
Market Equilibrium: Perfect Competition- Monopoly- Discriminating
Monopoly
Nature and Scope of Econometrics
Econometrics: Meaning, Scope, and Limitations - Methodology of
econometrics - Types of data: Time series, Cross section and panel data.
20%
Weightage
20%
Weightage
30%
Weightage
7
8
9
Module IV:
30%
Weightage
The Linear Regression Model
Origin and Modern interpretation- Significance of Stochastic Disturbance
term- Population Regression Function and Sample Regression FunctionAssumptions of Classical Linear regression model-Estimation of linear
Regression Model: Method of Ordinary Least Squares (OLS)- Test of
Significance of Regression coefficients : t test- Coefficient of Determination.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:
 Chiang A.C. and K. Wainwright, Fundamental Methods of Mathematical Economics, 4 th Edition, McGrawHill, New York, 2005. (cw)
 Dowling E.T, Introduction to Mathematical Economics, 2nd Edition, Schaum’s Series, McGraw- Hill, New
York, 2003(ETD)
 Damodar N.Gujarati, Basic Econometrics, McGraw-Hill, New York.
 Johnsonton J,- Econometric methods–McGraw Hill Company,NewYork
 Croxton F.E and Cowden D.J-Applied General Statistics-Prentice Hall of India Pvt Ltd.
 Henderson and Quandt, Microeconomic Theory, McGraw Hill Company,NewYork.
Annexure ‘AAB-CD-01’
Course Title: Modeling and Simulation
L
T
P/
SW/F
TOTAL
Course Code: to be decided later
Credit Units: 4
Level: PG
S
3
W
1
0
#
Course Title
1
Course Objectives:
Modeling and simulation is getting information about how something will
behave without actually testing it in real life. For instance, if we wanted to
design a racecar, but weren't sure what type of spoiler would improve
traction the most, we would be able to use a computer simulation of the car
to estimate the effect of different spoiler shapes on the coefficient of friction
in a turn. We're getting useful insights about different decisions we could
make for the car without actually building the car.
Prerequisites:
NIL
Student Learning Outcomes:
2
3


Weightage
(%)
The students will able to learn basic concepts of modeling and
about the formulation of the mathematical model.
The students will able to do comparative study of different
populations by using simulation.
Course Contents / Syllabus:
4 Module I:
20%
Weightage
Mathematical Model, types of Mathematical models and properties,
Procedure of modeling, Graphical method: Barterning model, Basic
optimization, Basic probability: Monte-Carlo simulation
5 Module II:
6
8
9
CREDIT
UNITS
4
Approaches to differential equation: Heun method, Local stability theory:
Bernoulli Trials, Classical and continuous models, Case studies in problems
of engineering and biological sciences.
Module III:
20%
Weightage
30%
Weightage
General techniques for simulating continuous random variables, simulation
from Normal and Gamma distributions, simulation from discrete probability
dstributions, simulating a non – homogeneous Poisson Process and queuing
system.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:
 Edward A. Bender. An Introduction to Mathematical Modeling.
 A. C. Fowler. Mathematical Models in Applied Sciences, Cambridge University Press.
 J. N. Kapoor. Mathematical Modeling, Wiley eastern Limited.
 S.M. Ross..Simulation, India Elsevier Publication.
 A.M.Law and W.D.Kelton.. Simulation Modeling and Analysis, T.M.H. Edition.
Annexure ‘AAB-CD-01’
Course Title: Statistical Genetics
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
The goal of the program is to provide an opportunity for Students will
receive an in depth training in the statistical foundations and methods of
analysis of genetic data, including genetic mapping, quantitative genetic
analysis, and design and analysis of medical genetic studies. They will
learn Population Genetics theory and Computational Molecular Biology.
Those not already having the necessary background will also study some
basic Genetics courses.
The primary goal of the program is to provide an opportunity for students
from the Mathematical, Statistical, and Computational Sciences to learn to
use their skills in the arena of molecular biology and genetic analysis.
2
Prerequisites:
NIL
Student Learning Outcomes:
3


0
TOTAL
CREDIT
UNITS
4
Weightage
(%)
The students will acquire the knowledge on the applications of
statistics in life sciences.
The sudents will able to do various statistical analyses for the given
biological data.
Course Contents / Syllabus:
4 Module I:
5
Functions of survival time, survival distributions and their applications viz.
exponential, gamma, weibull, Rayleigh, lognormal, death density function
for a distribution having bath-tub shape hazard function. Tests of goodness
of fit for survival distributions (WE test for exponential distribution, W-test
for lognormal distribution, Chi-square test for uncensored observations).
Module II:
6
Competing risk theory, Indices for measure-ment of probability of death
under competing risks and their inter-relations. Estimation of probabilities of
death under competing risks by maximum likelihood and modified
minimum Chi-square methods. Theory of independent and dependent risks.
Bivariate normal dependent risk model. Conditional death density functions.
Stochastic epidemic models: Simple and general epidemic models (by use of
random variable technique).
Module III:
7
Basic biological concepts in genetics, Mendels law, Hardy- Weinberg
equilibirium, random mating, distribution of allele frequency ( dominant/codominant cases), Approach to equilibirium for X-linked genes, natural
selection, mutation, genetic drift, equilibirium when both natural selection
and mutation are operative, detection and estimation of linkage in heredity.
Module IV:
Planning and design of clinical trials, Phase I, II, and III trials. Consideration
in planning a clinical trial, designs for comparative trials. Sample size
determination in fixed sample designs.
8
SW/F
W
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
9
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:













Biswas, S. (1995). Applied Stochastic Processes. A Biostatistical and Population Oriented Approach, Wiley
Eastern Ltd.
Collett, D. (2003). Modelling Survival Data in Medical Research, Chapman & Hall/CRC.
Cox, D.R. and Oakes, D. (1984). Analysis of Survival Data, Chapman and Hall.
Elandt Johnson R.C. (1971). Probability Models and Statistical Methods in Genetics, John Wiley & Sons.
Ewens, W. J. (1979). Mathematics of Population Genetics, Springer Verlag.
Ewens, W. J. and Grant, G.R. (2001). Statistical methods in Bio informatics: An Introduction, Springer.
Friedman, L.M., Furburg, C. and DeMets, D.L. (1998). Fundamentals of Clinical Trials, Springer Verlag.
Gross, A. J. And Clark V.A. (1975). Survival Distribution; Reliability Applications in Biomedical Sciences,
John Wiley & Sons.
Indrayan, A. (2008). Medical Biostatistics, Second Edition, Chapman & Hall/CRC.
Lee, Elisa, T. (1992). Statistical Methods for Survival Data Analysis, John Wiley & Sons.
Li, C.C. (1976). First Course of Population Genetics, Boxwood Press.
Miller, R.G. (1981). Survival Analysis, John Wiley & Sons.
Robert F. Woolson (1987). Statistical Methods for the analysis of biomedical data, John Wiley & Sons.
Annexure ‘AAB-CD-01’
Course Title: Reliability Theory and Applications
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
Reliability Course is a practical application of fundamental mechanical
engineering to system and component reliability. Designed for the
practitioner, this course covers the theories of mechanical reliability and
demonstrates the supporting mathematical theory. For the beginner, the
essential tools of reliability analysis are presented and demonstrated. These
applications are further solidified by practical problem solving and open
discussion. With the knowledge of the contents of the paper the students will
be able to apply this branch of Engineering Statistics very fruitfully in
industrial applications.

Prerequisites:
NIL
Student Learning Outcomes:
2
3
0
TOTAL
CREDIT
UNITS
4
Feedback
Rating
(on scale of
6 points)

The students will learn how to construct the systems for getting the
maximum reliability.
 The students will able to use different distributions for the study of
systems.
 The students will able to construct Life cycle curves.
Course Contents / Syllabus:
4 Module I:
5
Definition of Reliability function, hazard function & failure rate, pdf in form
of Hazard function, Reliability function and mean time to failure distribution
(MTTF) with DFR and IFR. Basic characterstics for exponential, normal and
lognormal, Weibull and gamma distribution, Loss of memory property of
exponential distribution
Module II:
6
Life cycle curves and probability distribution in modeling reliability,
Reliability of the system with independent limit connected in (a) Series (b)
parallel and (c) K out of n system.
Module III:
7
Reliability and mean life estimation based on failures time from (i) Complete
data (ii) Censored data with and without replacement of failed items
following exponential distribution [N C r],[N B r], [N B T], [N C(r, T)], [N
B(r T)].
Module IV:
8
9
Accelerated testing, types of acceleration and stress loading. Life stress
relationships. Arrhenius –lognormal, Arrhenius-Weibull, Arrheniusexponential models, Power-Weibull and Power-exponential models
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
70%
Text & References:
1. Sinha,S.K. (1980): Reliability and life testing, Wiley,Eastern Ltd.
2. Nelson, W. (1989): Accelerated Testing, Wiley.
3. Zacks: Introduction to reliability analysis, probability models and statistical, Springer-Verlag.
Annexure ‘AAB-CD-01’
Course Title: ACTUARIAL STATISTICS
Course Code: to be decided later
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Actuarial Science is the discipline that applies mathematical and statistical
methods to assess risk in the insurance and finance industries. In view of the
uncertainties involved, probability theory, statistics and economic theories
provide the foundation for developing and analysing actuarial models. Using
an appropriate stochastic model, simulation and high speed computing, it has
become possible to construct various tables and objectively determine the
premiums of different types of insurance contracts, even in the presence of
uncertainties associated with the prevailing risk factors. In such a decision
making process, statistical techniques play a central role. A strong statistical
background provides a good foundation for the integrated aspects of finance,
economics, risk management and insurance.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
SW/F
W
0
TOTAL
CREDIT
UNITS
4
Feedback
Rating
(on scale of
6 points)

The students will acquire the knowledge on various statistical
techniques in insuarance field.
 The students will able to compute risks for the given real life
situation.

The students will learn about the Life annuities.
Course Contents / Syllabus:
4 Module I:
5
Utility theory, insurance and utility theory, models for individual claims and
their sums, survival function, curtate future lifetime, force of mortality. Life
table and its relation with survival function, examples. Multiple life
functions, joint life and last survivor status.
Module II:
6
Multiple decrement models, deterministic and random survivorship groups,
associated single decrement tables, central rates of multiple decrement.
Distribution of aggregate claims, compound Poisson distribution and its
applications. Claim Amount distributions, approximating the individual
model, Stop-loss insurance.
Module III:
7
Principles of compound interest: Nominal and effective rates of interest and
discount, force of interestand discount, compound interest, accumulation
factor.
Life insurance: Insurance payable at the moment of death and at the end of
the year of death-level benefit insurance, endowment insurance, deferred
insurance and varying benefit insurance.
Life annuities: Single payment, continuous life annuities, discrete life
annuities, life annuities with monthly payments, varying annuities.
Module IV:
20%
Weightage
20%
Weightage
30%
Weightage
30%
Weightage
8
9
Net premiums: Continuous and discrete premiums, true monthly payment
premiums.
Net premium reserves: Continuous and discrete net premium reserves,
reserves on a semi continuous basis, reserves based on true monthly
premiums.
Lab
Problems based on All papers of Semester IV
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software
in a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop
down)
Weightage (%)
E
Ex
Mid-Term Exam
Project
Viva
Attendance
10%
10%
5%
5%
Text & References:



N.L. Bowers, H.U. Gerber J.C. Hickman, D.A. Jones mand C.J. Nesbitt, (1986): ‘Actuarial Mathematics’,
Society of Actuarial, Mathematics’, Society for Acturila, Ithaca, Illinois, U.S.A. Second Edition (1997).
Section I – Chapters: 1,2,3,8,9,11, 13. Section II – Chapters: 4,5,6,7.
Spurgeon E.T. (1972) : Life Contingencies, Cambridge University Press.
Neill, A. (1977) : Life Contingencies, Heineman.