Probability and Random Processes


Poisson Puffin

Spring 2024
Jiantao Jiao

Lecture: Tue & Thu 2:00 pm - 3:30 pm, Physics Building 4
Office Hour: Tue 4:00 pm - 5:00 pm, Cory 212

Announcements

Lecture Schedule

Schedule is subject to some changes.

Date Topics Readings
1/16 Introduction, Probability Spaces, Conditional Probability Theorem BT 1.1-1.3
1/18 Law of Total Probability, Bayes' Rule, Independence BT 1.4, 1.5
1/23 Discrete Random Variables: Bernoulli, Binomial, Geometric and Poisson Variables BT 2.1-2.3
1/25 Expectation, Variance, Conditional Expectation BT 2.4-2.6
1/30 Continuous Random Variables: Uniform, Exponential Variables BT 3.1, 3.2
2/1 Normal Random Variables, Multiple Random Variables, Conditioning BT 3.3-3.5
2/6 Continuous Bayes, Derived Distributions BT 3.6, 4.1
2/8 Covariance, Law of Iterated Expectation, Law of Total Variance BT 4.2-4.3
2/13 Moment Generating Function, Sum of Random Variables BT 4.4-4.6
2/15 Multivariate Gaussian, Concentration Inequalities, Weak Law of Large Numbers Multivariate Gaussian
BT 5.1, 5.2
2/20 Convergence in Probability, Distribution and Expectation Convergence
2/22 No Lecture
2/27 Midterm 1
2/29 Central Limit Theorem, Strong Law of Large Numbers BT 5.4-5.6, W 2.3, 3.2, 4.2
3/5 Discrete Time Markov Chains, States Classification BT 7.1, 7.2
3/7 DTMCs: Stationary Distribution, Hitting Time BT 7.3, 7.4, W 1.5
3/12 DTMCs: Reversibility, Big Theorem W 1.3, 2.5
Reversibility
3/14 Poisson Processes: Counting Process, Memorylessness, Splitting and Merging DTMC_review
BT 6.1, 6.2
3/19 Poisson Processes: Erlang Distribution, Random Incidence BT 6.2
3/21 Continuous Time Markov Chains: Rate Matrix and Stationary Distribution CTMCS
BT 7.5, W 6.2
3/26 Spring Break
3/28 Spring Break
4/2 MT2 Review
4/4 Midterm 2
4/9 CTMCs: Big Theorem, Jump Chain and Kolmogorov Equation CTMCS
BT 7.5, W 6.2
4/11 Bayesian Inference BT 8.1
4/16 Maximum a Posteriori Probability BT 8.2
4/18 Minimum Mean Square Error Estimate, Orthogonality, MMSE for Gaussian BT 8.3, W 9.6
4/23 Linear Least Square Estimate BT 8.4, 8.5, W 9.3
4/25 Maximum Likelihood Estimation, Linear Regression BT 9.1, 9.2, W 7.2, 9.4, 9.5