| 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 |