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
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