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Introduction to Probability (Spring 2018) (M-I-T)

Part I: The Fundamentals (M-I-T)

Lecture 1: Probability Models and Axioms (M-I-T)

Lecture 1 Supplement: Mathematical Background (M-I-T)

Lecture 2: Conditioning and Bayes' Rule (M-I-T)

Lecture 3: Independence (M-I-T)

Lecture 4: Counting (M-I-T)

Lecture 5: Discrete Random Variables Part I (M-I-T)

Lecture 6: Discrete Random Variables Part II (M-I-T)

Lecture 7: Discrete Random Variables Part III (M-I-T)

Lecture 8: Continuous Random Variables Part I (M-I-T)

Lecture 9: Continuous Random Variables Part II (M-I-T)

Lecture 10: Continuous Random Variables Part III (M-I-T)

Lecture 11: Derived Distributions (M-I-T)

Lecture 12: Sum of Independent R.V.s. Covariance and Correlation (M-I-T)

Lecture 13: Conditional Expectation & Variance Revisited; Sum of a Random Number of Independent R.V.s (M-I-T)

Part II: Inference & Limit Theorems (M-I-T)

Lecture 14: Introduction to Bayesian Inference (M-I-T)

Lecture 15: Linear Models With Normal Noise (M-I-T)

Lecture 16: Least Mean Squares (LMS) Estimation (M-I-T)

Lecture 17: Linear Least Mean Squares (LLMS) Estimation (M-I-T)

Lecture 18: Inequalities, Convergence, and the Weak Law of Large Numbers (M-I-T)

Lecture 19: The Central Limit Theorem (CLT) (M-I-T)

Lecture 20: An Introduction to Classical Statistics (M-I-T)

Part III: Random Processes (M-I-T)

Lecture 21: The Bernoulli Process (M-I-T)

Lecture 22: The Poisson Process Part I (M-I-T)

Lecture 23: The Poisson Process Part II (M-I-T)

Lecture 24: Finite-State Markov Chains (M-I-T)

Lecture 25: Steady–State Behavior of Markov Chains (M-I-T)

Lecture 26: Absorption Probabilities and Expected Time to Absorption (M-I-T)