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    Calendar

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

    SES # TOPICS KEY DATES
    L1 Introduction

    Probability Spaces    		  
    R1 Background Material from Analysis Problem set 1 out
    L2 Probability Measure, Lebesgue Measure  
    L3 Conditioning, Bayes Rule, Independence, Borel-Cantelli-Lemmas  
    R2 Measurability

    Borel-Cantelli    		 Problem set 1 due
    L4 Counting Problem set 2 out
    R3 Counting Exercises  
    L5 Measurable Functions, Random Variables, Cumulative Distribution Functions  
    L6 Discrete Random Variables, Expectation Problem set 2 due
    R4 Inclusion-exclusion Principle

    Pointwise Limit of Functions

    Random Variables    		 Problem set 3 out
    L7 Covariance and Correlation

    Inclusion-exclusion Principle    		  
    L8 Continuous Random Variables, Expectation  
    R5 Independence of RVs

    Continuous RV Sampling    		 Problem set 3 due
    L9 Continuous Random Variables, Joint Distributions, Bayes Rule  
    R6

    Expectation

    Order Statistics

    Bayes Rule

    Conjugate Distributions

    		 Problem set 4 out
    L10 Derived Distributions  
    L11 Abstract Integration  
    R7 Midterm Review Problem set 4 due
    L12 Monotone and Dominated Convergence

    Fatou's Lemma    		  
      Midterm Exam  
    L13 Product Measure, Fubini Theorem

    Abstract Definition of Conditional Expectation    		 Problem set 5 out
    R8 Fubini's Theorem  
    L14 Transforms: Moment Generating and Characteristic Functions Problem set 5 due
    L15 Multivariate Normal  
    R9 Continuity 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    		  
    L16 Multivariate Normal (cont.) Problem set 6 out
    L17 Weak Law of Large Numbers

    Central Limit Theorem    		 Problem set 6 due

    Problem set 7 out
    L18 Bernoulli and Poisson Processes  
    L19 Poisson Process (cont.) Problem set 8 out
    R10 Finite-state Markov Chains

    Convergence of Random Variables    		 Problem set 7 due
    L20 Finite-state Markov Chains  
    L21 Finite-state Markov Chains (cont.) Problem set 8 due

    Problem set 9 out
    L22 Finite-state Markov Chains (cont.)  
    L23 Convergence of Random Variables (cont.)  
    R11 Bernoulli and Poisson Processes Problem set 9 due

    Problem set 10 out
    L24 Strong Law of Large Numbers  
    L25 L2 Theory of Random Variables

    Construction of Conditional Expectations    		  
    L26 Miscellaneous Theoretical Topics Problem set 10 due
    L27 Large Deviations (Guest Lecture)  
      Review Session  
      Final Exam