MIT RES.6-012 Introduction to Probability, Spring 2018 (English) (Part 1)

   Wednesday, December 11, 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 1: L01.1 Lecture Overview

Lecture 2: L01.2 Sample Space

Lecture 3: L01.3 Sample Space Examples

Lecture 4: L01.4 Probability Axioms

Lecture 5: L01.5 Simple Properties of Probabilities

Lecture 6: L01.6 More Properties of Probabilities

Lecture 7: L01.7 A Discrete Example

Lecture 8: L01.8 A Continuous Example

Lecture 9: L01.9 Countable Additivity

Lecture 10: L01.10 Interpretations & Uses of Probabilities

Lecture 11: S01.0 Mathematical Background Overview

Lecture 12: S01.1 Sets

Lecture 13: S01.2 De Morgan's Laws

Lecture 14: S01.3 Sequences and their Limits

Lecture 15: S01.4 When Does a Sequence Converge

Lecture 16: S01.5 Infinite Series

Lecture 17: S01.6 The Geometric Series

Lecture 18: S01.7 About the Order of Summation in Series with Multiple Indices

Lecture 19: S01.8 Countable and Uncountable Sets

Lecture 20: S01.9 Proof That a Set of Real Numbers is Uncountable

Lecture 21: S01.10 Bonferroni's Inequality

Lecture 22: L02.1 Lecture Overview

Lecture 23: L02.2 Conditional Probabilities

Lecture 24: L02.3 A Die Roll Example

Lecture 25: L02.4 Conditional Probabilities Obey the Same Axioms

Lecture 26: L02.5 A Radar Example and Three Basic Tools

Lecture 27: L02.6 The Multiplication Rule

Lecture 28: L02.7 Total Probability Theorem

Lecture 29: L02.8 Bayes' Rule

Lecture 30: L03.1 Lecture Overview

Lecture 31: L03.2 A Coin Tossing Example

Lecture 32: L03.3 Independence of Two Events

Lecture 33: L03.4 Independence of Event Complements

Lecture 34: L03.5 Conditional Independence

Lecture 35: L03.6 Independence Versus Conditional Independence

Lecture 36: L03.7 Independence of a Collection of Events

Lecture 37: L03.8 Independence Versus Pairwise Independence

Lecture 38: L03.9 Reliability

Lecture 39: L03.10 The King's Sibling

Lecture 40: L04.1 Lecture Overview

Lecture 41: L04.2 The Counting Principle

Lecture 42: L04.3 Die Roll Example

Lecture 43: L04.4 Combinations

Lecture 44: L04.5 Binomial Probabilities

Lecture 45: L04.6 A Coin Tossing Example