Probability and Random Processes
TuTh 11-12:30 PM, Evans 10
- 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).
Lectures are not recorded. Subject to some changes.
|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
|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|