PracticuminAppliedProbability,APSTA-GE2351Fall2016
CourseTitle:APSTA-GE29xx:PracticuminAppliedProbability
NumberofCredits:1
MeetingPattern:1hourlectureperweek,14weeks;Falloffering.
CourseDescription:
Thisisacourseinthefoundationsofstatisticalinferencetechniques.Assumingsomeprior
exposuretofoundationalandintermediatestatisticalmethods,thiscoursewillfirstcovertopics
suchasKolgomorov’saxiomsofprobabilities,basicsofsettheory,discretecombinatorial
probability,Bayes’theorem,probabilitydistributionsandtheirpropertiesandassumptionsof
dependenceandindependence.Thesetopicsarefollowedbythefoundationaltopicsofstatistics:
samplingdistributions,thelawoflargenumbersandthecentrallimittheorem.Thiscoursewillmix
theoreticalapproacheswithsimulation-basedillustrationsofthesemaintopics.Thestudentwillbe
expectedtounderstandthemathematicaltheoryandapplythetopicscoveredtoproblemsolving
viaanalyticalandsimulationbasedmethodsinstatisticalprogramminglanguagesuchasR.
CoursePrerequisites/Expectations:
•
REQUIRED:anintroductorycourseinprobabilityandstatistics(non-calculusbased)suchas
APSTAT-GE2001and2002.NOTE:Co-enrollmentinSTAT-GB3301satisfiesthisrequirement.
• Werecommendthiscoursefor1styearMS-A3SRstudentswithoutpriorexperienceincalculusbasedprobability(forexample,coursessuchasSTAT-GB3301)
CourseStructure/Format:
•
Eachweek,selected problems from the corresponding textbook sections will be solved analytically and
•
then via simulation to demonstrate the connections between the approaches.
Students will work collaboratively in class to complete simulation assignments to concepts covered in
the course.
LearningObjectives:
Bytheendofthecourse,studentswillbeableto:
1. Demonstrateanunderstandingofprobabilitythroughproblemsolvingandsimulationapproaches.
2. Demonstrateanunderstandingofstatisticaldistributiontheory,emphasizingthepropertiesofand
relationshipsamongrandomvariables.
3. Demonstrateanunderstandingofsamplingdistributionsandidentifytheroleofasymptoticsand
variabilityinstatisticalinference.
CourseRequirements:
Thegradeforthiscoursewillbedeterminedasfollows:
•
•
•
Classparticipation(30%)
Groupsimulationassignments(50%)
Individualproject(20%)
1
PracticuminAppliedProbability,APSTA-GE2351Fall2016
GradingScheme:
Thefollowingsystemwillbeusedtoconvertnumericalgradestolettergrades:
A
AB+
B
BC+
C
CD+
D
F
92.5 – 100
89.5 – 92.5
86.5 – 89.5
82.5 – 86.5
79.5 – 82.5
76.5 – 79.5
72.5 – 76.5
69.5 – 72.5
66.5 – 69.5
62.5 – 66.5
0 – 62.5
RequiredReadingsand/orText(apartialreadinglist)
Required:Hogg,R.V.,McKean,J.W.,andCraig,A.T.(2013)"IntroductiontoMathematicalStatistics",
seventhedition,NewJersey:PrenticeHall.
AcademicIntegrity:
AllstudentsareresponsibleforunderstandingandcomplyingwiththeNYUSteinhardtStatementon
AcademicIntegrity.Acopyisavailableat:http://steinhardt.nyu.edu/policies/academic_integrity.
StudentswithDisabilities:
StudentswithphysicalorlearningdisabilitiesarerequiredtoregisterwiththeMosesCenterfor
StudentswithDisabilities,726Broadway,2ndFloor,(212-998-4980andonlineat
http://www.nyu.edu/csd)andarerequiredtopresentaletterfromtheCentertotheinstructoratthe
startofthesemesterinordertobeconsideredforappropriateaccommodation.
Week
1
2,3
Topic
4
5
6
7
8
9
10-11
12-13
14
MathematicalExpectation
MultivariateDistributions
SpecialDistributions(Discrete)
SpecialDistributions(NormalRelated)
SpecialDistributions(Normal)
SpecialDistributions(MultivariateNormal)
Distributionsoffunctionsofrandomvariables
LimitTheorems
PointEstimation
General Concepts of Probability
Random Variables, Probability Functions And Distribution
Functions
Readingsfromcoursetext
Chapter1,sections1–4
Chapter1,sections5-7
Chapter1,sections8–10
Chapter2
Chapter3,sections1-2
Chapter3,sections3,6
Chapter3,section4
Chapter3,section5
Chapter4
Chapter5
Chapter6,section1
2