# Probability and Random Processes

Fall 2023
Jiantao Jiao

Lecture: Tue & Thu 11:00 am - 12:29 pm, Valley Life Sciences 2060
Office Hour: Tue 1:30 pm - 2:30 pm, Cory-212 (1:00-2:00 pm on 09/05, 10/24)

## 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 in the course but not added to Ed after a few days, please email eecs126-fall23 (at) lists.eecs.berkeley.edu.
• 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.

08/24 Introduction, Probability Spaces, Conditional Probability, Law of Total Probability B-T 1
08/29 Independence, Bayes Rule, Discrete Random Variables B-T 1, 2
Random Variables
08/31 Expectation, Uniform, Geometric, Binomial and Poisson Distributions B-T 2
09/05 Variance, Conditional / Iterated Expectation B-T 2
09/07 Continuous Probability, Uniform, Exponential Distributions B-T 3
09/12 Gaussian Distribution, Derived Distributions, Continuous Bayes B-T 3, 4.1-4.2
09/14 Covariance, Gaussian Distribution B-T 4.3-4.6
09/19 Multivariate Gaussian, MGFs, Concentration Inequalities (Markov, Chebyshev) B-T 4.4, 5.1,
Multivariate Gaussian
09/21 Convergence B-T 5.2-5.3, W 2.2-2.3
Convergence
09/26 No Lecture (Midterm 1)
09/28 No Lecture
10/03 Weak and Strong Law of Large Numbers, Central Limit Theorem B-T 5.2-5.5, W 2.2-2.3
10/05 Information Theory Information Theory
10/10 Discrete Time Markov Chains, Stationary Distribution, Hitting Time, First Step Equations (I) W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4
Markov Chains
10/12 Discrete Time Markov Chains, Stationary Distribution, Hitting Time, First Step Equations (II) W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4
Markov Chains
10/17 DTMCs: Reversibility, Infinite States, Classification, Big Theorem W 1.3, 2.5
Reversibility
10/19 Poisson Processes: Counting Process, Memorylessness, Erlang Distribution, Merging, Splitting B-T 6.1-6.3, W 13.4
Poisson Process
10/24 Random Incidence, Review of DTMC and PP midterm2_review_problems
Poisson Process
10/26 Continuous Time Markov Chains: Rate Matrix and Stationary Distribution B-T 7.5, W 13.5
CTMCS
10/31 No Lecture (Midterm 2)
11/02 CTMCs: Big Theorem, First Step Equations and Jump Chain B-T 7.5, W 13.5
CTMCS
11/07 Erdos-Renyi Random Graphs Random Graphs
11/09 Maximum a Posteriori Estimation B-T 8.1-8.2
11/14 Maximum Likelihood Estimation, Statistical Hypothesis Testing, Neyman-Pearson Lemma Hypothesis Testing
B-T 9.1
11/16 Linear Least Square Estimate, Vector Space of Random Variables Hilbert space of RVs
B-T 8.3-8.5, W 7.1-7.5
11/21 Minimum Mean Square Error Estimation W 7.1-7.5, W 8.1
11/23 No Lecture (Thanksgiving)
11/28 Orthogonal Updates and Kalman Filters W 7.6, 8.1-8.3
Kalman Filter (1)
Kalman Filter (2)
11/30 Hidden Markov Models W 11
Hidden Markov Models