# Probability and Random Processes

Fall 2019
Shyam Parekh
TuTh 11-12:30 PM, Evans 10

## Announcements

• Lab 2 has been uploaded and is due Friday 9/20.
• Homework 3 has been uploaded and is due FRIDAY 9/20.
• Lab 1 Solutions have been uploaded and self grades are due Monday 9/16.
• Homework 2 Solutions have been uploaded and self grades are due Monday 9/16.
• Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 95RY4R).

## Lecture Schedule

Lectures are not recorded. Subject to some changes.

Date Topics Reading Assignments
08/29 Introduction, Probability Spaces, Conditional Probability, Law of Total Probability B-T 1 HW 1
HW 1 Sol
09/03 Independence, Bayes Rule, Discrete Random Variables B-T 1, 2 Lab 0
Lab 0 Sol
09/05 Expectation, Uniform, Geometric, Binomial and Poisson Distributions B-T 2 HW 2
HW 2 Sol
09/10 (Co)variance, Correlation, Conditional / Iterated Expectation, Entropy B-T 2 Lab 1
Lab 1 Sol
09/12 Entropy, Continuous Probability, Uniform, Exponential Distributions B-T 3 HW 3
Lab 2
09/17 Gaussian Distribution, Derived Distributions, Continuous Bayes B-T 3, 4.1-4.2 TBA
09/19 Order Statistics, Convolution, Moment Generating Functions B-T 4.3-4.6 TBA
09/24 MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) B-T 5.1 & W 13.7 TBA
09/26 No Lecture (Midterm 1)   TBA
10/01 Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem B-T 5.2-5.6, W 2.1-2.3 TBA
10/03 CLT, Information Theory, Capacity of the Binary Erasure Channel (BEC) Capacity of a BEC TBA
10/08 Achievability of BEC Capacity, Markov Chains Introduction W 1, 13.3, B-T 7.1-7.4 TBA
10/10 Discrete Time Markov Chains: Invariant Distribution and Balance Equations W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4 TBA
10/15 DTMCs: Hitting Time, First Step Eqs (FSEs), Infinite States, Classification, Big Theorem W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4, Markov Chains TBA
10/17 DTMCs: Classification, Reversibility, Poisson Processes: Construction B-T 6.1-6.3, W 13.4, Reversibility TBA
10/22 Poisson Processes: Counting Process, Memorylessness, Merging, Splitting B-T 6.1-6.3, W 13.4 TBA
10/24 PP: Erlang Distribution, Random Incidence, Continuous Time Markov Chains Intro, Rate Matrix B-T 7.5, W 13.5 TBA
10/29 CTMCs: Balance Equations, Big Theorem, FSEs B-T 7.5, W 13.5 TBA
10/31 CTMCs: Simulated DTMC, Erdos-Renyi Random Graphs Random Graphs TBA
11/05 No Lecture (Midterm 2)   TBA
11/07 Maximum Likelihood Estimation, Maximum A Posteriori Estimation W 5.1, B-T 8.1-8.2, 9.1 TBA
11/12 MLE/MAP, Neyman Pearson Hypothesis Testing W 5.1, B-T 8.1-8.2, 9.1/ W 5.5-5.6, 6.5, B-T 9.3-9.4, Hypothesis Testing TBA
11/14 Vector Space of Random Variables and Least Squares Estimation W 5.5-5.6, 6.5, B-T 9.3-9.4/ W 7.1-7.5, B-T 8.3-8.5 Hilbert Space of Random Variables TBA
11/19 Linear Least Squares Estimation, Minimum Mean Square Error (MMSE) Estimation W 7.1-7.5, B-T 8.3-8.5 TBA
11/21 MMSE, Gram Schmidt Process W 7.1-7.5, W 8.1 TBA
11/26 Jointly Gaussian Random Variables, Kalman Filter W 6.3-6.4, 7.6, 8.1-8.3 Geometric Derivation of Scalar Kalman Filter TBA
11/28 No Lecture (Thanksgiving)   TBA
12/03 Kalman Filter W 7.6, 8.1-8.3 TBA
12/05 Hidden Markov Models W 9.2,9.4 HMMs and the Viterbi Algorithm TBA