MIT RES.6-012 Introduction to Probability, Spring 2018 (English) (Part 3)

   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 91: L09.3 Conditioning Example

Lecture 92: L09.4 Memorylessness of the Exponential PDF

Lecture 93: L09.5 Total Probability & Expectation Theorems

Lecture 94: L09.6 Mixed Random Variables

Lecture 95: L09.7 Joint PDFs

Lecture 96: L09.8 From The Joint to the Marginal

Lecture 97: L09.9 Continuous Analogs of Various Properties

Lecture 98: L09.10 Joint CDFs

Lecture 99: S09.1 Buffon's Needle & Monte Carlo Simulation

Lecture 100: L10.1 Lecture Overview

Lecture 101: L10.2 Conditional PDFs

Lecture 102: L10.3 Comments on Conditional PDFs

Lecture 103: L10.4 Total Probability & Total Expectation Theorems

Lecture 104: L10.5 Independence

Lecture 105: L10.6 Stick-Breaking Example

Lecture 106: L10.7 Independent Normals

Lecture 107: L10.8 Bayes Rule Variations

Lecture 108: L10.9 Mixed Bayes Rule

Lecture 109: L10.10 Detection of a Binary Signal

Lecture 110: L10.11 Inference of the Bias of a Coin

Lecture 111: L11.1 Lecture Overview

Lecture 112: L11.2 The PMF of a Function of a Discrete Random Variable

Lecture 113: L11.3 A Linear Function of a Continuous Random Variable

Lecture 114: L11.4 A Linear Function of a Normal Random Variable

Lecture 115: L11.5 The PDF of a General Function

Lecture 116: L11.6 The Monotonic Case

Lecture 117: L11.7 The Intuition for the Monotonic Case

Lecture 118: L11.8 A Nonmonotonic Example

Lecture 119: L11.9 The PDF of a Function of Multiple Random Variables

Lecture 120: S11.1 Simulation

Lecture 121: L12.1 Lecture Overview

Lecture 122: L12.2 The Sum of Independent Discrete Random Variables

Lecture 123: L12.3 The Sum of Independent Continuous Random Variables

Lecture 124: L12.4 The Sum of Independent Normal Random Variables

Lecture 125: L12.5 Covariance

Lecture 126: L12.6 Covariance Properties

Lecture 127: L12.7 The Variance of the Sum of Random Variables

Lecture 128: L12.8 The Correlation Coefficient

Lecture 129: L12.9 Proof of Key Properties of the Correlation Coefficient

Lecture 130: L12.10 Interpreting the Correlation Coefficient

Lecture 131: L12.11 Correlations Matter

Lecture 132: L13.1 Lecture Overview

Lecture 133: L13.2 Conditional Expectation as a Random Variable

Lecture 134: L13.3 The Law of Iterated Expectations

Lecture 135: L13.4 Stick-Breaking Revisited