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 23.1 - Overview
VIDEO
Lecture 23.1 - Overview
Lecture 23.2 - The Sum of Independent Poisson Random Variables
Lecture 23.3 - Merging Independent Poisson Processes
Lecture 23.4 - Where is an Arrival of the Merged Process Coming From?
Lecture 23.5 - The Time until the First (or Last) Lightbulb Burns Out
Lecture 23.6 - Splitting a Poisson Process
Lecture 23.7 - Random Incidence in the Poisson Process
Lecture 23.8 - Random Incidence in a Non-Poisson Process
Lecture 23.9 - Different Sampling Methods can Give Different Results
Lecture 23.10 - Poisson vs Normal Approximations to the Binomial
Lecture 23.11 - Poisson Arrivals during an Exponential Interval
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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