| 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 |
|