MIT RES.6-012 Introduction to Probability, Spring 2018 (English) (Part 5)

   Thursday, December 12, 2024   

Starting a new Lecture Notes Series on MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015

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MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 By Lecture Notes together!

Lecture 181: L18.2 The Markov Inequality

Lecture 182: L18.3 The Chebyshev Inequality

Lecture 183: L18.4 The Weak Law of Large Numbers

Lecture 184: L18.5 Polling

Lecture 185: L18.6 Convergence in Probability

Lecture 186: L18.7 Convergence in Probability Examples

Lecture 187: L18.8 Related Topics

Lecture 188: S18.1 Convergence in Probability of the Sum of Two Random Variables

Lecture 189: S18.2 Jensen's Inequality

Lecture 190: S18.3 Hoeffding's Inequality

Lecture 191: L19.1 Lecture Overview

Lecture 192: L19.2 The Central Limit Theorem

Lecture 193: L19.3 Discussion of the CLT

Lecture 194: L19.4 Illustration of the CLT

Lecture 195: L19.5 CLT Examples

Lecture 196: L19.6 Normal Approximation to the Binomial

Lecture 197: L19.7 Polling Revisited

Lecture 198: L20.1 Lecture Overview

Lecture 199: L20.2 Overview of the Classical Statistical Framework

Lecture 200: L20.3 The Sample Mean and Some Terminology

Lecture 201: L20.4 On the Mean Squared Error of an Estimator

Lecture 202: L20.5 Confidence Intervals

Lecture 203: L20.6 Confidence Intervals for the Estimation of the Mean

Lecture 204: L20.7 Confidence Intervals for the Mean, When the Variance is Unknown

Lecture 205: L20.8 Other Natural Estimators

Lecture 206: L20.9 Maximum Likelihood Estimation

Lecture 207: L20.10 Maximum Likelihood Estimation Examples

Lecture 208: L21.1 Lecture Overview

Lecture 209: L21.2 The Bernoulli Process

Lecture 210: L21.3 Stochastic Processes

Lecture 211: L21.4 Review of Known Properties of the Bernoulli Process

Lecture 212: L21.5 The Fresh Start Property

Lecture 213: L21.6 Example: The Distribution of a Busy Period

Lecture 214: L21.7 The Time of the K-th Arrival

Lecture 215: L21.8 Merging of Bernoulli Processes

Lecture 216: L21.9 Splitting a Bernoulli Process

Lecture 217: L21.10 The Poisson Approximation to the Binomial

Lecture 218: L22.1 Lecture Overview

Lecture 219: L22.2 Definition of the Poisson Process

Lecture 220: L22.3 Applications of the Poisson Process

Lecture 221: L22.4 The Poisson PMF for the Number of Arrivals

Lecture 222: L22.5 The Mean and Variance of the Number of Arrivals

Lecture 223: L22.6 A Simple Example

Lecture 224: L22.7 Time of the K-th Arrival

Lecture 225: L22.8 The Fresh Start Property and Its Implications