Probability And Random Variables

Topic outline

• 

  General

  Probability And Random Variables
  
  

  Instructor:	Elif Uysal

  
  Added: 21 February 2011

  
  

  To watch videos via YouTube:

   
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  Topic 1

  Introduction to probability theory; Review of set theory

  • Lecture1 File
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  Topic 2

  Probability Spaces; Axioms and properties or probability

  • Lecture 2 File
  • Week 2 | Hour 1 [Video] File
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  Topic 3

  Discrete and Continuous Probability Laws, Conditional Probability

  • Week 2 | Hour 2 [Video] File
  • Week 2 | Hour 3 [Video] File
  • Lecture 3 File
  • Lecture 3 -single page per sheet File
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  Topic 4

  Total Probability Theorem, Bayes's Rule

  • Week 3 | Hour 1 [Video] File
  • lecture 4 File
  • lecture 4-single page per sheet File
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  Topic 5

  Independence, Conditional Independence

  • Week 3 | Hour 2 [Video] File
  • Week 3 | Hour 3 [Video] File
  • lecture 5 File
  • lecture 5-single page per sheet File
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  Topic 6

  Independent Trials, Counting

  • lecture 6 File
  • lecture 6-single page per sheet File
  • Week 4 - Hour 1 [Video] File
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  Topic 7

  Discrete Random Variables

  • lecture 7 File
  • lecture 7-single page per sheet File
  • Week 4 - Hour 2 [Video] File
  • Week 4 - Hour 3 [Video] File
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  Topic 8

  Expectation and Variance

  • lecture 8 File
  • lecture 8-single page per sheet File
  • Week 5 - Hour 1 [Video] File
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  Topic 9

  Properties of Expectation and Variance, Joint PMFs

  • lecture 9 File
  • lecture 9-single page per sheet File
  • Week 5 - Hour 2 [Video] File
  • Week 5 - Hour 3 [Video] File
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  Topic 10

  Conditional PMFs

  • lecture 10 File
  • Week 6 - Hour 1 [Video] File
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  Topic 11

  Conditioning one Random Variable on another; conditional expectation

  • lecture 11 File
  • lecture 11-single page per sheet File
  • Week 6 - Hour 2 [Video] File
  • Week 6 - Hour 3 [Video] File
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  Topic 12

  Iterated Expectation; Independence of a random variable from an event

  • Week 7 - Hour 1 [Video] File
  • lecture 12 File
  • lecture 12-single page per sheet File
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  Topic 13

  Independence of Random Variables

  • Week 7 - Hour 2 [Video] File
  • Week 7 - Hour 3 [Video] File
  • lecture 13 File
  • Lecture 13 -single page per sheet File
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  Topic 14

  Continuous Random Variables

  • Week 8 - Hour 1 [Video] File
  • lecture 14 File
  • Lecture 14 - single page per sheet File
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  Topic 15

  Expectation and the Cumulative Distribution Function

  • Week 8 - Hour 2 [Video] File
  • Week 8 - Hour 3 [Video] File
  • Lecture 15 - single page per sheet File
  • Lecture 15 File
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  Topic 16

  The Gaussian CDF

  • lecture 16 File
  • Lecture 16 -single page per sheet File
  • Week 9 - Hour 1 [Video] File
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  Topic 17

  Conditional PDFs, Joint PDFs

  • Lecture 17 -single page per sheet File
  • Lecture 17 File
  • Week 9 - Hour 2 [Video] File
  • Week 9 - Hour 3 [Video] File
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  Topic 18

  Conditioning one random variable on another

  • Lecture 18 -single page per sheet File
  • Lecture 18 File
  • Week 10 - Hour 1 [Video] File
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  Topic 19

  Independence, Continuous Bayes's Rule; Derived Distributions

  • Lecture 19 -single page per sheet File
  • Lecture 19 File
  • Week 10 - Hour 2 [Video] File
  • Week 10 - Hour 3 [Video] File
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  Topic 20

  Derived Distributions

  • Lecture 20 File
  • Lecture 20 -single page per sheet File
  • Week 11 - Hour 1 [Video] File
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  Topic 21

  Functions of Two Random Variables; Correlation and Covariance

  • Lecture 21 File
  • Lecture 21 -single page per sheet File
  • Week 11 - Hour 2 [Video] File
  • Week 11 - Hour 3 [Video] File
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  Topic 22

  Applications of Covariance

  • Lecture 22 File
  • Week 12 - Hour 1 [Video] File
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  Topic 23

  Transforms (Moment Generating Functions)

  • Lecture 23 File
  • Lecture 23- single page per sheet File
  • Week 12 - Hour 2 [Video] File
  • Week 12 - Hour 3 [Video] File
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  Topic 24

  Markov and Chebychev Inequalities, Convergence In Probability

  • Lecture 24 File
  • Lecture 24-single page per sheet File
  • Week 13 - Hour 1 [Video] File
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  Topic 25

  The Weak Law of Large Numbers

  • Week 13 - Hour 2 [Video] File
  • Lecture 25- single page per sheet File
  • Lecture 25 File
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  Topic 26

  The Central Limit Theorem

  • Week 13 - Hour 3 [Part 1] [Video] File
  • Week 13 - Hour 3 [Part 2] [Video] File
  • Lecture 26- single page per sheet File
  • Lecture 26 File
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  Topic 27

  The Bernoulli Process

  • Week 14 - Hour 1 [Video] File
  • Lecture 27 File
  • Lecture 27- single page per sheet File
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  Topic 28

  The Poisson Process

  • Week 14 - Hour 2 [Video] File
  • Week 14 - Hour 3 [Video] File
  • Lecture 28 File
  • Lecture 28- single page per sheet File
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  Topic 29
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  Topic 30