Date | Topic | Reading | Notes | |
1 | Tue Aug 07 | Introduction. Set theory review. Sample spaces, events, probabilities. | BT 1.1-1.2 | |
2 | Thu Aug 09 | Conditional probability. Multiplication rule, total probability theorem, Bayes' rule. | BT 1.3-1.4 | |
3 | Tue Aug 14 | Independence | BT 1.5 | |
4 | Thu Aug 16 | Counting | BT 1.6 | |
5 | Tue Aug 21 | Discrete random variables. Probability mass functions. Expectation, variance. | BT 2.1-2.4 | Assignment 1 due |
6 | Thu Aug 23 | Multiple discrete random variables: joint PMFs, conditional & marginal PMFs, conditional expectation. | BT 2.5-2.6 | |
7 | Tue Aug 28 | Multiple discrete random variables: independence, covariance, correlation. | BT 2.7, 4.2 | |
8 | Thu Aug 30 | Continuous random variables. Probability density functions, cumulative distribution functions. | BT 3.1-3.2 | |
9 | Tue Sep 04 | Multiple continuous random variables: conditioning, independence. | BT 3.3-3.5 | Assignment 2 due |
10 | Thu Sep 06 | Continuous random variables: further examples. | BT 3.6 | |
Tue Sep 11 | Midterm 1 (in class) | |||
11 | Thu Sep 13 | Further topics on random variables: derived distributions. | BT 4.1 | |
Tue Sep 18 | Class canceled. | |||
12 | Thu Sep 20 | Further topics on random variables: iterated expectations, moment generating functions. | BT 4.3-4.5, GS Ch 5 | Assignment 3 due |
13 | Tue Sep 25 | Further topics on random variables: concentration inequalities. | BT 5.1, class notes | |
14 | Thu Sep 27 | Convergence of random variables. Laws of large numbers. | BT 5.2-5.3, class notes, GS Ch 7 | |
Tue Oct 02 | Institute Holiday (Gandhi Jayanti) | |||
15 | Thu Oct 04 | Central limit theorem | BT 5.4 | |
16 | Tue Oct 09 | Bernoulli and Poisson processes | BT Ch 6 | Assignment 4 due |
17 | Thu Oct 11 | Markov chains: introduction, classification of states, steady-state probabilities. | BT 7.1-7.2 | |
Tue Oct 16 | Midterm 2 (in class) | |||
18 | Thu Oct 18 | Markov chains: probabilities of absorption, expected time to absorption. | BT 7.3-7.4 | |
19 | Tue Oct 23 | Selected applications of probability in computer science: Randomized algorithms Guest lecture by Dr. Neeldhara Misra |
Lecture notes | |
20 | Thu Oct 25 | Statistics I. Parameter estimation: bias, consistency, mean squared error; maximum likelihood estimator; confidence intervals. | BT 9.1 Note on confidence intervals |
Assignment 5 due |
21 | Tue Oct 30 | Statistics II. Hypothesis testing: Type I and II errors; likelihood ratio tests; Neyman-Pearson lemma. | BT 9.3-9.4, class notes | |
Thu Nov 01 | Institute Holiday (Kannada Rajyotsava) | |||
22 | Tue Nov 06 | Statistics III. Bayesian inference: prior and posterior distribution; conjugate priors. | BT 8.1, class notes | |
23 | Thu Nov 08 | Statistics IV. Bayesian point estimates: MAP estimator, conditional expectation estimator. Bayesian binary hypothesis testing: MAP decision rule. | BT 8.2-8.3 | |
Tue Nov 13 | Institute Holiday (Diwali) | |||
24 | Thu Nov 15 | Fun with Probability: Review & Preview | Assignment 6 due | |
Tue 27 Nov | Final exam (9:00-12:00, CLH L1) |