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MIT RES.6-012 Introduction to Probability, Spring 2018

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Last updated on Apr 24, 2018
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L01.1 Lecture Overview
1:52
L01.2 Sample Space
5:38
L01.3 Sample Space Examples
5:03
L01.4 Probability Axioms
8:55
L01.5 Simple Properties of Probabilities
11:05
L01.6 More Properties of Probabilities
8:40
L01.7 A Discrete Example
5:13
L01.8 A Continuous Example
5:20
L01.9 Countable Additivity
12:10
L01.10 Interpretations & Uses of Probabilities
3:48
S01.0 Mathematical Background Overview
1:25
S01.1 Sets
10:55
S01.2 De Morgan's Laws
4:53
S01.3 Sequences and their Limits
6:00
S01.4 When Does a Sequence Converge
2:46
S01.5 Infinite Series
3:11
S01.6 The Geometric Series
4:07
S01.7 About the Order of Summation in Series with Multiple Indices
10:05
S01.8 Countable and Uncountable Sets
6:19
S01.9 Proof That a Set of Real Numbers is Uncountable
4:02
S01.10 Bonferroni's Inequality
9:28
L02.1 Lecture Overview
2:07
L02.2 Conditional Probabilities
9:00
L02.3 A Die Roll Example
5:02
L02.4 Conditional Probabilities Obey the Same Axioms
7:45
L02.5 A Radar Example and Three Basic Tools
10:59
L02.6 The Multiplication Rule
6:17
L02.7 Total Probability Theorem
5:25
L02.8 Bayes' Rule
4:28
L03.1 Lecture Overview
1:26
L03.2 A Coin Tossing Example
7:59
L03.3 Independence of Two Events
6:10
L03.4 Independence of Event Complements
2:59
L03.5 Conditional Independence
2:46
L03.6 Independence Versus Conditional Independence
5:30
L03.7 Independence of a Collection of Events
6:00
L03.8 Independence Versus Pairwise Independence
8:35
L03.9 Reliability
7:28
L03.10 The King's Sibling
6:54
L04.1 Lecture Overview
2:29
L04.2 The Counting Principle
11:12
L04.3 Die Roll Example
4:39
L04.4 Combinations
10:08
L04.5 Binomial Probabilities
6:38
L04.6 A Coin Tossing Example
11:48
L04.7 Partitions
5:20
L04.8 Each Person Gets An Ace
9:45
L04.9 Multinomial Probabilities
10:36
L05.1 Lecture Overview
1:40
L05.2 Definition of Random Variables
9:14
L05.3 Probability Mass Functions
10:21
L05.4 Bernoulli & Indicator Random Variables
3:06
L05.5 Uniform Random Variables
4:06
L05.6 Binomial Random Variables
6:08
L05.7 Geometric Random Variables
7:37
L05.8 Expectation
10:38
L05.9 Elementary Properties of Expectation
4:12
L05.10 The Expected Value Rule
10:00
L05.11 Linearity of Expectations
3:59
S05.1 Supplement: Functions
8:08
L06.1 Lecture Overview
2:02
L06.2 Variance
10:43
L06.3 The Variance of the Bernoulli & The Uniform
8:40
L06.4 Conditional PMFs & Expectations Given an Event
7:31
L06.5 Total Expectation Theorem
6:28
L06.6 Geometric PMF Memorylessness & Expectation
10:29
L06.7 Joint PMFs and the Expected Value Rule
10:16
L06.8 Linearity of Expectations & The Mean of the Binomial
8:25
L07.1 Lecture Overview
1:50
L07.2 Conditional PMFs
10:48
L07.3 Conditional Expectation & the Total Expectation Theorem
6:10
L07.4 Independence of Random Variables
5:08
L07.5 Example
4:44
L07.6 Independence & Expectations
4:22
L07.7 Independence, Variances & the Binomial Variance
7:09
L07.8 The Hat Problem
16:09
S07.1 The Inclusion-Exclusion Formula
11:13
S07.2 The Variance of the Geometric
5:42
S07.3 Independence of Random Variables Versus Independence of Events
6:51
L08.1 Lecture Overview
1:13
L08.2 Probability Density Functions
11:09
L08.3 Uniform & Piecewise Constant PDFs
2:52
L08.4 Means & Variances
6:57
L08.5 Mean & Variance of the Uniform
3:56
L08.6 Exponential Random Variables
8:09
L08.7 Cumulative Distribution Functions
12:48
L08.8 Normal Random Variables
9:14
L08.9 Calculation of Normal Probabilities
10:11
L09.1 Lecture Overview
1:33
L09.2 Conditioning A Continuous Random Variable on an Event
9:56
L09.3 Conditioning Example
3:08
L09.4 Memorylessness of the Exponential PDF
8:18
L09.5 Total Probability & Expectation Theorems
6:51
L09.6 Mixed Random Variables
5:35
L09.7 Joint PDFs
9:18
L09.8 From The Joint to the Marginal
7:23
L09.9 Continuous Analogs of Various Properties
1:40
L09.10 Joint CDFs
4:16
S09.1 Buffon's Needle & Monte Carlo Simulation
16:12
L10.1 Lecture Overview
1:42