# Probability and Random Processes

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

• Welcome to EECS 126! Please read the course info for logistics. We will be syncing Ed with the course roster periodically. If you are newly enrolled but not added to Ed after a few days, please email eecs126-spr24@lists.eecs.berkeley.edu and provide your student ID. We will use Gradescope for all submissions/grade-related items. If you are not added automatically, please use the code 4GZG68 to join.
• Time conflicts are allowed only if you choose to attend EECS 126 lectures. The lectures are not recorded and midterms will be held during lecture times. There will be no alternative final exam time. Please make sure that your exam times don't conflict with other classes you're taking!

## Lecture Schedule

Schedule is subject to some changes.

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