Probability and Random Processes
Fall 2019
Shyam Parekh
TuTh 1112:30 PM, Evans 10
Announcements
 Optional Labs Sol have been released. Self grades are due Friday (12/20) here.
 HW 13 Sol has been posted. Self grades are due Friday night (12/20) here.
 Final Review Guide made by Kevin.
 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  BT 1  HW 1 HW 1 Sol 
09/03  Independence, Bayes Rule, Discrete Random Variables  BT 1, 2  Lab 0 Lab 0 Sol 
09/05  Expectation, Uniform, Geometric, Binomial and Poisson Distributions  BT 2  HW 2 HW 2 Sol 
09/10  (Co)variance, Correlation, Conditional / Iterated Expectation, Entropy  BT 2  Lab 1 Lab 1 Sol 
09/12  Entropy, Continuous Probability, Uniform, Exponential Distributions  BT 3  HW 3 HW 3 Sol Lab 2 Lab 2 Sol 
09/17  Gaussian Distribution, Derived Distributions, Continuous Bayes  BT 3, 4.14.2  TBA 
09/19  Order Statistics, Convolution, Moment Generating Functions  BT 4.34.6  HW 4 (Optional) HW 4 Sol 
09/24  MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff)  BT 5.1 & W 13.7  HW 5 HW 5 Sol 
09/26  No Lecture (Midterm 1)  MT 1 MT 1 Sol 

10/01  Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem  BT 5.25.6, W 2.12.3  HW 6 HW 6 Sol 
10/03  CLT, Information Theory, Capacity of the Binary Erasure Channel (BEC)  Capacity of a BEC  Lab 3 Lab 3 Sol 
10/08  Achievability of BEC Capacity, Markov Chains Introduction  W 1, 13.3, BT 7.17.4  
10/10  No Lecture (Power Outage)  HW 7 HW 7 Sol 

10/15  Discrete Time Markov Chains, Classification, Stationary Distribution  W 1, 2.4, 2.6, 13.3, BT 7.17.4  HW 8 HW 8 Sol 
10/17  DTMCs: Hitting Time, First Step Eqs (FSEs), Infinite States, Classification, Big Theorem  W 1, 2.4, 2.6, 13.3, BT 7.17.4, Markov Chains  Lab 4 Lab 4 Sol 
10/22  DTMCs: Classification, Reversibility, Poisson Processes: Construction  BT 6.16.3, W 13.4, Reversibility  HW 9 HW 9 Sol 
10/24  Poisson Processes: Counting Process, Memorylessness, Merging, Splitting  BT 6.16.3, W 13.4  
10/29  PP: Erlang Distribution, Random Incidence, Continuous Time Markov Chains Intro, Rate Matrix  BT 7.5, W 13.5  
10/31  CTMCs: Balance Equations, Big Theorem, FSEs  BT 7.5, W 13.5  HW 10 HW 10 Sol 
11/05  No Lecture (Midterm 2)  MT2 MT2 Sol 

11/07  CTMCs: Simulated DTMC, ErdosRenyi Random Graphs  Random Graphs  HW 11 HW 11 Sol 
11/12  Maximum Likelihood Estimation, Maximum A Posteriori Estimation  W 5.1, BT 8.18.2, 9.1  
11/14  MLE/MAP, Neyman Pearson Hypothesis Testing  W 5.1, BT 8.18.2, 9.1/ W 5.55.6, 6.5, BT 9.39.4, Hypothesis Testing  HW 12 HW 12 Sol 
11/19  Vector Space of Random Variables and Least Squares Estimation  W 5.55.6, 6.5, BT 9.39.4/ W 7.17.5, BT 8.38.5 Hilbert Space of Random Variables  
11/21  Linear Least Squares Estimation, Minimum Mean Square Error (MMSE) Estimation  W 7.17.5, BT 8.38.5  
11/26  MMSE, Gram Schmidt Process  W 7.17.5, W 8.1  
11/28  No Lecture (Thanksgiving)  
12/03  Jointly Gaussian Random Variables, Kalman Filter  W 6.36.4, 7.6, 8.18.3 Geometric Derivation of Scalar Kalman Filter  HW 13 HW 13 Sol 
12/05  Kalman Filter  W 7.6, 8.18.3  TBA 