Res.6012 Introduction to Probability
Res.6012 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)

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  FiniteState Markov Chains 
Lecture 25  SteadyState Behavior of Markov Chains 
Lecture 26  Absorption Probabilities and Expected Time to Absorption 
References 
Res.6012 Introduction to Probability
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.
