Probability and Random Processes

Spring 2020
Kannan Ramchandran
TuTh 12:30-2 PM, Lewis 100

OH: Tuesday 2-3 Cory 212


Lecture Schedule

Lectures are not recorded. Subject to some changes.

Date Topics Reading Assignments
1/21 Introduction, Probability Spaces, Conditional Probability, Law of Total Probability B-T 1 HW 1
HW 1 Sol
1/23 Independence, Bayes Rule, Discrete Random Variables B-T 1, 2 Lab 0
Lab 0 Sol
1/28 Expectation, Uniform, Geometric, Binomial and Poisson Distributions B-T 2 HW 2
HW 2 Sol
1/30 (Co)variance, Correlation, Conditional / Iterated Expectation, Law of Total Variance B-T 2 Lab 1
Lab 1 Sol
2/4 Continuous Probability, Uniform, Exponential Distributions B-T 3 HW 3
HW 3 Sol
2/6 Gaussian Distribution, Derived Distributions, Continuous Bayes B-T 3, 4.1-4.2 Lab 2
Lab 2 Sol
2/11 Order Statistics, Convolution, Moment Generating Functions B-T 4.3-4.6 HW 4
2/13 MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) B-T 5.1 TBA
2/18 Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem Convergence TBA
2/20 No Lecture (Midterm 2/21)    
2/25 Information Theory Information Theory TBA
2/27 Binary Erasure Channel Capacity Capacity of BEC TBA
3/3 Discrete Time Markov Chains, Calculations, Stationary Distribution Markov Chains TBA
3/5 DTMCs: Infinite States, Classification, Big Theorem   TBA
3/10 DTMCs: Reversibility, Hitting Time, First Step Equations Reversibility TBA
3/12 Poisson Processes: Counting Process, Memorylessness, Merging, Splitting   TBA
3/17 PP: Erlang Distribution, Random Incidence   TBA
3/19 Continuous Time Markov Chains: Rate Matrix and Stationary Distribution   TBA
3/31 CTMCs: Big Theorem, First Step Equations and Jump Chain   TBA
4/2 No Lecture (Midterm 4/3)    
4/7 Erdos-Renyi Random Graphs Random Graphs TBA
4/9 Maximum Likelihood Estimation, Maximum a Posteriori Estimation   TBA
4/14 Statistical Hypothesis Testing, Neyman-Pearson Lemma Hypothesis Testing TBA
4/16 Minimum Mean Square Error Estimation, Vector Space of Random Variables Hilbert Space TBA
4/21 Linear Least Square Estimate   TBA
4/23 Jointly Guassian Random Variables   TBA
4/28 Orthogonal Updates and Kalman Filter Geometric Derivation of Scalar Kalman Filter TBA
4/30 Fisher Information and Cramer Rao Bound   TBA