Probability Theory

Course

Scores: 20% + 30% + 50% Probability Theory Midterm Probability Theory Final

Contents

Random Variables

General Definition of Probability Conditional Probability Random Variables Continuous Random Variables

Joint Distributions

Transformations of Random Variables

Distributions

Distributions of Random Variables

Characteristics

Mathematical Expectation Variance Conditional Expectation Covariance and Correlation

Law of the Unconscious Statistician (LOTUS)

Law of Large Numbers Central Limit Theorem

Statistics

Statistics Parameters Estimation Hypothesis Test Neyman-Pearson Lemma Pearson's chi-squared Test

Theorems

Jensen's Inequality Hoeffding's Inequality

Additional

Maximum Likelihood Estimation (MLE) Maximum a Posteriori Probability (MAP) Evidence Lower Bound (ELBO) Variational Inference