Probability and Random Processes
TuTh 12:30-2 PM, Lewis 100
OH: Tuesday 2-3 Cory 212
- Lab 6 is released. It is due by Friday night (4/10) at 11:59PM.
- Homework 9 solutions are released. Self grades are due by Wednesday night (4/8) at 11:59PM.
- Homework 10 is released. It is due by Wednesday night (4/8) at 11:59PM.
- Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 9XJ64Z).
Lectures are not recorded. Subject to some changes.
|1/21||Introduction, Probability Spaces, Conditional Probability, Law of Total Probability||B-T 1|
|1/23||Independence, Bayes Rule, Discrete Random Variables||B-T 1, 2|
|1/28||Expectation, Uniform, Geometric, Binomial and Poisson Distributions||B-T 2|
|1/30||(Co)variance, Correlation, Conditional / Iterated Expectation, Law of Total Variance||B-T 2|
|2/4||Continuous Probability, Uniform, Exponential Distributions||B-T 3|
|2/6||Gaussian Distribution, Derived Distributions, Continuous Bayes||B-T 3, 4.1-4.2|
|2/11||Order Statistics, Convolution, Moment Generating Functions||B-T 4.3-4.6|
|2/13||MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff)||B-T 5.1|
|2/18||Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem||B-T 5.2-5.6, W 2.1-2.3
|2/20||No Lecture (Midterm 2/21)|
|2/25||Information Theory||Information Theory|
|2/27||Binary Erasure Channel Capacity||W 1, 13.3, B-T 7.1-7.4
Capacity of BEC
|3/3||Information Theory Wrapup||W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4
|3/5||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|
|3/10||DTMCs: Reversibility, Infinite States, Classification, Big Theorem||Reversibility|
|3/12||Poisson Processes: Counting Process, Memorylessness, Merging, Splitting||B-T 6.1-6.3, W 13.4|
|3/17||PP: Erlang Distribution, Random Incidence||B-T 6.1-6.3, W 13.4|
|3/19||Continuous Time Markov Chains: Rate Matrix and Stationary Distribution||B-T 7.5, W 13.5|
|3/31||CTMCs: Big Theorem, First Step Equations and Jump Chain||B-T 7.5, W 13.5|
|4/2||No Lecture (Midterm 4/3)|
|4/7||Erdos-Renyi Random Graphs||Random Graphs|
|4/9||Maximum Likelihood Estimation, Maximum a Posteriori Estimation||B-T 8.1-8.2, 9.1, W 5.1|
|4/14||Statistical Hypothesis Testing, Neyman-Pearson Lemma||Hypothesis Testing|
|4/16||Minimum Mean Square Error Estimation, Vector Space of Random Variables||Hilbert Space|
|4/21||Linear Least Square Estimate|
|4/23||Jointly Gaussian Random Variables|
|4/28||Orthogonal Updates and Kalman Filter||Geometric Derivation
of Scalar Kalman Filter
|4/30||Fisher Information and Cramer Rao Bound|