# Probability and Random Processes

Fall 2022
Kannan Ramchandran
Lecture: TuTh 12:30-2 PM (Birge 50)
Office Hours: Tu 2-3 PM (Cory 212)

## Announcements

• Time conflicts will be allowed for this course but there will not be an alternate 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.

08/25 Introduction, Probability Spaces, Conditional Probability, Law of Total Probability B-T 1
08/30 Independence, Bayes Rule, Discrete Random Variables B-T 1, 2
Random Variables
09/01 Expectation, Uniform, Geometric, Binomial and Poisson Distributions B-T 2
09/06 (Co)variance, Correlation, Conditional / Iterated Expectation, Law of Total Variance B-T 2
09/08 Continuous Probability, Uniform, Exponential Distributions B-T 3
09/13 Gaussian Distribution, Derived Distributions, Continuous Bayes B-T 3, 4.1-4.2
09/15 Order Statistics, Convolution, Moment Generating Functions B-T 4.3-4.6
09/20 MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) B-T 5.1
09/22 Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem B-T 5.2-5.6, W 2.1-2.3
Convergence
09/27 Information Theory Information Theory
09/29 No Lecture (Midterm)
10/04 Binary Erasure Channel Capacity W 1, 13.3, B-T 7.1-7.4
Capacity
10/06 Information Theory Wrapup
10/11 Discrete Time Markov Chains, Stationary Distribution, Hitting Time, First Step Equations W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4
Markov Chains
10/13 DTMCs: Reversibility, Infinite States, Classification, Big Theorem Reversibility
10/18 DTMC Wrapup B-T 6.1-6.3, W 13.4
10/20 Poisson Processes: Counting Process, Memorylessness, Merging, Splitting B-T 6.1-6.3, W 13.4
Poisson Process
10/25 PP: Erlang Distribution, Random Incidence B-T 6.1-6.3, W 13.4
10/27 Continuous Time Markov Chains: Rate Matrix and Stationary Distribution B-T 7.5, W 13.5
11/01 CTMCs: Big Theorem, First Step Equations and Jump Chain B-T 7.5, W 13.5
CTMCS
11/03 No Lecture (Midterm)
11/08 Erdos-Renyi Random Graphs Random Graphs
11/10 Maximum Likelihood Estimation, Maximum a Posteriori Estimation B-T 8.1-8.2, 9.1, W 5.1
11/15 Statistical Hypothesis Testing, Neyman-Pearson Lemma Hypothesis Testing
B-T 9.3-9.4, W 5.5-5.6, 6.5
11/17 Linear Least Square Estimate, Vector Space of Random Variables Hilbert space of RVs
B-T 8.3-8.5, W 7.1-7.5
11/22 Minimum Mean Square Error Estimation W 7.1-7.5, W 8.1
11/29 Jointly Gaussian Random Variables W 6.3-6.4, 7.6, 8.1-8.3
Jointly Gaussian RVs
12/1 Orthogonal Updates and Kalman Filter W 7.6, 8.1-8.3
Kalman Filter (1)
Kalman Filter (2)