Lahore University of Management Sciences
CS 501 Applied Probability
(Cross-listed as: CMPE 501/EE 515/MATH 439)
Fall 2012-13
Instructor
Room No.
Office Hours
Webpage
Email
Telephone
TAs
TA Office Hours
Course URL (if any)
Dr. Ihsan Ayyub Qazi
SSE 9-114A
TBA
http://web.lums.edu.pk/~ihsan
[email protected]
+92 42 3560 8368
TBA
TBA
LMS (https://lms.lums.edu.pk)
Course Basics
Credit Hours
Lecture(s)
Tutorial (per week)
3
2 Per Week
1 Per Week
Course Distribution
Core
Elective
Open for Student Category
Close for Student Category
MS Computer Science
Electrical Engineering, Computer Engineering, and Math Majors
All
None
Duration
Duration
75 mins
60 mins
COURSE DESCRIPTION
How does Google rank webpages in its search results? How are social networks, such as Twitter, able to handle billions of queries
every day with large traffic fluctuations? Why simply changing the order of processing of jobs on a computer can reduce latency?
What is the risk of using a new medical treatment? How likely is it to rain one week from now?
An underlying theme in the above questions is the need for decision-making in the presence of uncertainty. Probability theory
allows us to model uncertainty and analyze its effects. Consequently, probability theory plays a central role in fields such as
computer science, engineering, management and social sciences where uncertain situations occur frequently. This course deals
with the nature, formulation, and analysis of probabilistic situations. It will introduce the fundamentals of probability with special
emphasis on applications. The course will provide a rigorous understanding of probability concepts including: Random Variables,
Expectations, Joint Distributions, Limit Theorems, Stochastic Processes, Markov Chains, and Queuing Theory.
COURSE PREREQUISITE(S)
Good preparation in Calculus
•
COURSE OBJECTIVES
To teach students the fundamentals of probability theory
•
To introduce students to real-world applications of probability theory
•
To trains students in applying probability concepts for solving real world problems
•
Learning Outcomes
Students will have a solid understanding of probability concepts
•
Students will be able to apply probability concepts to solve real-world problems
•
Students will become aware of several real-world applications of probability
•
Grading Breakup and Policy
Quizzes: 20%
Assignments: 20%
Midterm Examination: 25%
Final Examination: 35%
Lahore University of Management Sciences
Examination Detail
Yes/No: Yes
Duration: 3 hours
Midterm
Preferred Date: TBA
Exam
Exam Specifications: TBA
Yes/No: Yes
Duration: 3 hours
Final Exam
Exam Specifications: TBA
Textbook(s)/Supplementary Readings
Required Text
•
Introduction to Probability by Bertsekas and Tsitsiklis.
Optional Texts
•
Probability and Random Processes for Electrical Engineering by Alberto Leon Garcia
•
Introduction to Probability and Statistics for Engineers and Scientists by Sheldon Ross
•
Introduction to Probability Models by Sheldon Ross
•
Stochastic Processes by Sheldon Ross
Session
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Topics
Course Overview, Sample Space, Events, Counting
Conditional Probability, Independence, Bayes’ Rule
Discrete Random Variables (RVS): Basic Concepts, PMF, Bernoulli RV
Common Discrete RVs (Binomial, Geometric, Poisson)
Functions of RVs, Expectation, Mean, Variance
Joint Distributions and Conditional Distributions
Continuous RVs: Basic Concepts, PDF, CDF, Uniform RV
Common Continuous RVs (Exponential, Normal, Pareto [Optional])
Moment Generating Functions, Sums of RVs, Correlation, and Covariance
Limit Theorems (Markov, Chebychev, and Chernoff)
Limit Theorems (Markov, Chebychev, and Chernoff) Wrap-up
Sample paths, Convergence, & Law of Large Numbers (Weak and Strong)
Law of Large Numbers Wrap up + Central Limit Theorem
MIDTERM EXAM
Bernoulli Process: Inter-arrival Times, Kth Arrival Time, Splitting and Merging
Poisson Process: Inter-arrival Times, Kth Arrival Time, Splitting and Merging
Finite-state Discrete-Time Markov Chains (DTMC)
Finite-state DTMCs Wrap-up + Infinite-state DTMCs
Infinite-state DTMC Wrap-up
Google Search and the Page Rank Algorithm
Continuous-Time Markov Chains (CTMC): Translating CTMCs to DTMCs
CTMC: Interpretation of CTMCs, Examples of CTMCs
Introduction to Queuing Theory, Kendall’s Notation, Little’s Law
M/M/1, M/M/1/K (Optional) Queuing Systems
PASTA, M/M/m, M/M/m/m
M/G/1, Introduction to Scheduling Theory
Parameter Estimation, Maximum Likelihood Estimation, Confidence Intervals
Final Topics + Course Review
Recommended Readings
Chapters 1.1, 1.2, & 1.6
Chapters 1.3, 1.4, & 1.5
Chapters 2.1 & 2.2
Chapters 2.2
Chapters 2.3 & 2.4
Chapters 2.5 & 2.6
Chapters 3.1 & 3.2
Chapters 3.1 & 3.3
Chapters 4.1, 4.2, & 4.5
Chapters 7.1
Chapters 7.1 + Notes
Chapters 7.2-7.5
Chapters 7.2-7.5
Chapter 5.1
Chapter 5.2
Chapter 6.1
Chapter 6.2-6.3 + Notes
Chapter 6.2-6.3 + Notes
Notes
Chapter 6.4 + Notes
Notes
Notes
Notes
Notes
Notes
Notes