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Res.6-012 Introduction to Probability

Res.6-012 Introduction to Probability (Spring 2018, MIT OCW). Instructors: Prof. John Tsitsiklis and Prof. Patrick Jaillet. 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. (from ocw.mit.edu)

Lecture 16.1 - Overview

Go to the Course Home or watch other lectures:

Part I: The Fundamentals

Lecture 01 - Probability Models and Axioms

Lecture s01 - Supplement: Mathematical Background

Lecture 02 - Conditioning and Bayes' Rule

Lecture 03 - Independence

Lecture 04 - Counting

Lecture 05 - Discrete Random Variables, Part I

Lecture 06 - Discrete Random Variables, Part II

Lecture 07 - Discrete Random Variables, Part III

Lecture 08 - Continuous Random Variables, Part I

Lecture 09 - Continuous Random Variables, Part II

Lecture 10 - Continuous Random Variables, Part III

Lecture 11 - Derived Distributions

Lecture 12 - Sum of Independent Random Variables Covariance and Correlation

Lecture 13 - Conditional Expectation and Variance Revisited

Part II: Inference and Limit Theorems

Lecture 14 - Introduction to Bayesian Inference

Lecture 15 - Linear Modes and Normal Noise

Lecture 16 - Least Mean Squares (LMS) Estimation

Lecture 17 - Linear Least Mean Squares (LLMS) Estimation

Lecture 18 - Inequalities, Convergence, and the Weak Law of Large Numbers

Lecture 19 - The Central Limit Theorem (CLT)

Lecture 20 - An Introduction to Classical Statistics

Part III: Random Processes

Lecture 21 - The Bernoulli Process

Lecture 22 - The Poisson Process, Part I

Lecture 23 - The Poisson Process, Part II

Lecture 24 - Finite-State Markov Chains

Lecture 25 - Steady-State Behavior of Markov Chains

Lecture 26 - Absorption Probabilities and Expected Time to Absorption