EECS 126

Probability and Random Processes

Notes taken in Professor Thomas Courtade's Spring 2023 EECS 126 course.

CS 189*  /  CS 188*  /  EE 120  /  EECS 151*  /  EECS 127  /  EECS 126  /  EECS 16B  /  EECS 16A*  /  MATH H53

1. Introduction: Logistics, Probability Basics
2. Bayes Rule, Independence, Discrete Random Variables
3. Expectation (Linearity, Tail Sum), Discrete Distributions
4. Sum of Independent Binomials, Variance, Covariance, Correlation Coefficient, Conditional Expectation and Iterated Expectation, Entropy
5. Entropy, Continuous Probability (Sample Space, Events, PDFs, CDFs), Continuous Distributions
6. Gaussian Distribution, Derived Distributions, Continuous Bayes
7. Order Statistics, Convolution, Moment Generating Functions
8. MGFs, Bounds:Concentration Inequalities (Markov, Chebyshev, Chernoff)
9. Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem
10. Information Theory and Digital Communication, Capacity of the Binary Erasure Channel (BEC)
11. Achievability of BEC Capacity, Markov Chains Introduction
12. No notes
13. No notes
14. DTMCs: Classification, Reversibility, Poisson Processes: Construction
15. Poisson Processes Counting Process, Memorylessness, Merging, Splitting
16. Poisson Processes Erlang Distribution, Random Incidence, Continuous Time Markov Chains Introduction, Rate Matrix
17. CTMCs Balance Equations, Big Theorem, FSEs
18. CTMCs Simulated DTMC, Erdos-Renyi Random Graphs
19. Maximum Likelihood Estimation, Maximum A Posteriori Estimation
20. No notes
21. Neyman Pearson Hypothesis Testing, Vector Space of Random Variables and Least Squares Estimation
22. Linear Least Squares Estimation, Minimum Mean Square Error MMSE Estimation
23. No notes
24. Jointly Gaussian Random Variables, Kalman Filter
25. Kalman Filter
26. Course Recap

• Course Summary

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