My notes for when I took this course in Fall 2025, taught by Preeya Khanna.

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Please submit any errors you might find in the errata, thank you!

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Phoenix Wilson

Course by Week

Week Topics
1 Probability Space
2 Conditional Probability, Independence, Random Variables
3 Expectation, Variance, Joint Distributions, Conditioning Random Variables
4 Continuous Random Variables, Derived Distributions
5 Convolution, Covariance, Iterated Expectation, Conditional Variance, Estimators, Moment Generating Transform
6 Concentration Inequalities
7 Convergence, Law of Large Numbers, Central Limit Theorem
8 Bernoulli, Poisson Processes
9 Discrete Time Markov Chains
10 Continuous Time Markov Chains
11 Statistical Inference, Point Estimates, Confidence Intervals, t-Distribution, Linear Regression, Hypothesis Testing
13 Jointly Gaussians
14 Kalman Filter
15 Hidden Markov Models

Probability Space

Conditional Probability, Independence, Random Variables

Expectation, Variance, Joint Distributions, Conditioning Random Variables

Continuous Random Variables, Derived Distributions

Convolution, Covariance, Iterated Expectation, Conditional Variance, Estimators, Moment Generating Transform

Concentration Inequalities

Convergence, Law of Large Numbers, Central Limit Theorem

Bernoulli, Poisson Processes

Discrete Time Markov Chains

Continuous Time Markov Chains

Statistical Inference, Point Estimates, Confidence Intervals, t-Distribution, Linear Regression, Hypothesis Testing

Jointly Gaussians

Kalman Filter