Course Topics

1. Probability Basics
   1. Probability and Counting
   2. Infinite Sample Spaces | Axioms of Probability
   3. Conditional Probability | Independence
   4. Bayes' Rule
2. Random Variables
   1. Random Variables | Expectation | Binomial Distrbution
   2. Geometric Dist | Functions of RV
   3. Variance | Conditioning | Multiple RVs
   4. Linearity of Expectation
3. Advanced Random Variables
   1. Tail Bounds (Markov, Chebyshev, Chernoff)
   2. Continuos Distributions
   3. Central Limit Theorem
4. Advanced Topics and Applications
   1. Statistics
   2. Markov Chains
   3. Multidimensional Gaussians | Kalman Filters