Probability in Data

Basic Probability

Conditional Probability

Probability Distributions

Expected Value

Variance and Standard Deviation

Joint and Marginal Probability Distributions

Covariance and Correlation

Sampling Distributions

Hypothesis Testing: Principles and P-values

Confidence Intervals for Parameter Estimation

Law of Large Numbers

Central Limit Theorem

Bayes' Theorem and Bayesian Inference

Monte Carlo Simulation for Probability

Maximum Likelihood Estimation

Foundations of Linear Regression: Probabilistic View

Markov Chains and Applications

Information Theory: Entropy and Mutual Information

Resampling Methods: Bootstrapping and Permutation Tests

Advanced Bayesian Inference: MCMC and Model Comparison