Calendar

The calendar below provides information on the course's lecture (L), recitation (R), and tutorial (T) sessions.

Ses # Topics Key Dates
L1 Probability Models and Axioms Problem set 1 out
R1 Set Notation, Terms and Operators (include De Morgan's), Sample Spaces, Events, Probability Axioms and Probability Laws
L2 Conditioning and Bayes' Rule
R2 Conditional Probability, Multiplication Rule, Total Probability Theorem, Baye's Rule
L3 Independence Problem set 1 due

Problem set 2 out
R3 Introduction to Independence, Conditional Independence
T1 Baye's Theorem, Independence and Pairwise Independence
L4 Counting
L5 Discrete Random Variables; Probability Mass Functions; Expectations Problem set 2 due

Problem set 3 out
R4 Counting; Discrete Random Variables, PMFs, Expectations
T2 Probability, PMF, Means, Variances, and Independence
L6 Conditional Expectation; Examples
R5 Conditional Expectation, Examples
L7 Multiple Discrete Random Variables Problem set 3 due

Problem set 4 out
R6 Multiple Discrete Random Variables, PMF
T3 PMF, Conditioning and Independence
L8 Continuous Random Variables - I
R7 Continuous Random Variables, PMF, CDF
L9 Continuous Random Variables - II Problem set 4 due

Problem set 5 out
R8 Marginal, Conditional Densities/Expected Values/Variances
T4 Expectation and Variance, CDF Function, Expectation Theorem, Baye's Theorem
L10 Continuous Random Variables and Derived Distributions
Quiz 1 (Covers up to Lec #1-8 Inclusive)
T5 Random Variables, Density Functions
L11 More on Continuous Random Variables, Derived Distributions, Convolution
R9 Derivation of the PMF/CDF from CDF, Derivation of Distributions from Convolutions (Discrete and Continuous)
L12 Transforms Problem set 5 due

Problem set 6 out
R10 Transforms, Properties and Uses
T6 Transforms, Simple Continuous Convolution Problem
L13 Iterated Expectations
R11 Iterated Expectations, Random Sum of Random Variables
L13A Sum of a Random Number of Random Variables Problem set 6 due

Problem set 7 out
R12 Expected Value and Variance
T7 Iterated Expectation, Covariance/Independence with Gaussians, Random Sum of Random Variables
L14 Prediction; Covariance and Correlation
R13 Recitation 13
R14 Prediction; Covariance and Correlation
L15 Weak Law of Large Numbers Problem set 7 due

Problem set 8 out
R15 Weak Law of Large Numbers
T8 Correlation, Estimation, Convergence in Probability
Quiz 2 (Covers up to and Including Lec #14)
T9 Signal-to-Noise Ratio, Chebyshev Inequality
L16 Bernoulli Process
R16 Bernoulli Process, Split Bernoulli Process
L17 Poisson Process Problem set 8 due

Problem set 9 out
R17 Poisson Process, Concatenation of Disconnected Intervals
T10 Two Instructive Drill Problems (One Bernoulli, One Poisson)
L18 Poisson Process Examples
R18 Competing Exponentials, Poisson Arrivals
L19 Markov Chains - I Problem set 9 due

Problem set 10 out
R19 Markov Chain, Recurrent State
T11 Poisson Process, Conditional Expectation, Markov Chain
L20 Markov Chains - II
R20 Steady State Probabilities, Formulating a Markov Chain Model
L21 Markov Chains - III Problem set 10 due

Problem set 11 out

Problem set 11 due two days after Lec #21
R21 Conditional Probabilities for a Birth-death Process
T12 Markov Chains: Steady State Behavior and Absorption Probabilities
L22 Central Limit Theorem
R22 Central Limit Theorem
L23 Central Limit Theorem (cont.), Strong Law of Large Numbers
R23 Last Recitation, Review Material Covered after Quiz 2 (Chapters 5-7)
Final Exam