Courses:

Fundamentals of Probability >> Content Detail



Calendar / Schedule



Calendar

The calendar below provides information on the course's lecture (L) and recitation (R) sessions.


SES #TOPICSKEY DATES
L1Introduction

Probability Spaces
R1Background Material from AnalysisProblem set 1 out
L2Probability Measure, Lebesgue Measure
L3Conditioning, Bayes Rule, Independence, Borel-Cantelli-Lemmas
R2Measurability

Borel-Cantelli
Problem set 1 due
L4CountingProblem set 2 out
R3Counting Exercises
L5Measurable Functions, Random Variables, Cumulative Distribution Functions
L6Discrete Random Variables, ExpectationProblem set 2 due
R4Inclusion-exclusion Principle

Pointwise Limit of Functions

Random Variables
Problem set 3 out
L7Covariance and Correlation

Inclusion-exclusion Principle
L8Continuous Random Variables, Expectation
R5Independence of RVs

Continuous RV Sampling
Problem set 3 due
L9Continuous Random Variables, Joint Distributions, Bayes Rule
R6

Expectation

Order Statistics

Bayes Rule

Conjugate Distributions

Problem set 4 out
L10Derived Distributions
L11Abstract Integration
R7Midterm ReviewProblem set 4 due
L12Monotone and Dominated Convergence

Fatou's Lemma
Midterm Exam
L13Product Measure, Fubini Theorem

Abstract Definition of Conditional Expectation
Problem set 5 out
R8Fubini's Theorem
L14Transforms: Moment Generating and Characteristic FunctionsProblem set 5 due
L15Multivariate Normal
R9Continuity of the Characteristic Function

Variance of Random Sum of Random Variables

Sum of a Geometric Number of Exponential Random Variables

Gaussian Random Vector

Bayes Rule
L16Multivariate Normal (cont.)Problem set 6 out
L17Weak Law of Large Numbers

Central Limit Theorem
Problem set 6 due

Problem set 7 out
L18Bernoulli and Poisson Processes
L19Poisson Process (cont.)Problem set 8 out
R10Finite-state Markov Chains

Convergence of Random Variables
Problem set 7 due
L20Finite-state Markov Chains
L21Finite-state Markov Chains (cont.)Problem set 8 due

Problem set 9 out
L22Finite-state Markov Chains (cont.)
L23Convergence of Random Variables (cont.)
R11Bernoulli and Poisson ProcessesProblem set 9 due

Problem set 10 out
L24Strong Law of Large Numbers
L25L2 Theory of Random Variables

Construction of Conditional Expectations
L26Miscellaneous Theoretical TopicsProblem set 10 due
L27Large Deviations (Guest Lecture)
Review Session
Final Exam

 








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