Introduction to Probability

The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management. This resource is a companion site to [6.041SC Probabilistic Systems Analysis and Applied Probability](/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/). It covers the same content, using videos developed for an {{% resource_link "b12b31ce-02f6-4ea1-bc55-cb8e089f7b2f" "edX" %}} version of the course.

Syllabus

Introduction to Probability, Selected Textbook Summary Material
Lecture 1 Supplement: Mathematical Background
Lecture 1: Probability Models and Axioms
Lecture 1: Probability Models and Axioms
Lecture 2: Conditioning and Bayes' Rule
Lecture 2: Conditioning and Bayes' Rule
Lecture 3: Independence
Lecture 3: Independence
Lecture 4: Counting
Lecture 4: Counting
Lecture 5: Discrete Random Variables Part I
Lecture 5: Discrete Random Variables Part I
Lecture 6: Discrete Random Variables Part II
Lecture 6: Discrete Random Variables Part II
Lecture 7: Discrete Random Variables Part III
Lecture 7: Discrete Random Variables Part III
Lecture 8: Continuous Random Variables Part I
Lecture 8: Continuous Random Variables Part I
Lecture 9: Continuous Random Variables Part II
Lecture 9: Continuous Random Variables Part II
Lecture 10: Continuous Random Variables Part III
Lecture 10: Continuous Random Variables Part III
Lecture 11: Derived Distributions
Lecture 11: Derived Distributions
Lecture 12: Sum of Independent R.V.s. Covariance and Correlation
Lecture 12: Sum of Independent R.V.s. Covariance and Correlation
Lecture 13: Conditional Expectation & Variance Revisited; Sum of a Random Number of Independent R.V.s
Lecture 13: Conditional Expectation & Variance Revisited; Sum of a Random Number of Independent R.V.s
Lecture 14: Introduction to Bayesian Inference
Lecture 14: Introduction to Bayesian Inference
Lecture 15: Linear Models With Normal Noise
Lecture 15: Linear Models With Normal Noise
Lecture 16: Least Mean Squares (LMS) Estimation
Lecture 16: Least Mean Squares (LMS) Estimation
Lecture 17: Linear Least Mean Squares (LLMS) Estimation
Lecture 17: Linear Least Mean Squares (LLMS) Estimation
Lecture 18: Inequalities, Convergence, and the Weak Law of Large Numbers
Lecture 18: Inequalities, Convergence, and the Weak Law of Large Numbers
Lecture 19: The Central Limit Theorem (CLT)
Lecture 19: The Central Limit Theorem (CLT)
Lecture 20: An Introduction to Classical Statistics
Lecture 20: An Introduction to Classical Statistics
Lecture 21: The Bernoulli Process
Lecture 21: The Bernoulli Process
Lecture 22: The Poisson Process Part I
Lecture 22: The Poisson Process Part I
Lecture 23: The Poisson Process Part II
Lecture 23: The Poisson Process Part II
Lecture 24: Finite-State Markov Chains
Lecture 24: Finite-State Markov Chains
Lecture 25: Steady-State Behavior of Markov Chains
Lecture 25: Steady-State Behavior of Markov Chains
Lecture 26: Absorption Probabilities and Expected Time to Absorption
Lecture 26: Absorption Probabilities and Expected Time to Absorption