Topic outline

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  Probability And Random Variables
  
  

  Instructor:	Elif Uysal-Bıyıkoğlu

  
  Added: 21 February 2011
• 1
  
  
  Introduction to probability theory; Review of set theory

  • Lecture1 File

  
  
• 2
  
  
  Probability Spaces; Axioms and properties or probability

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

  
  
• 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

  
  
• 4
  
  
  Total Probability Theorem, Bayes's Rule

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

  
  
• 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

  
  
• 6
  
  
  Independent Trials, Counting

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

  
  
• 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

  
  
• 8
  
  
  Expectation and Variance

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

  
  
• 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

  
  
• 10
  
  
  Conditional PMFs

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

  
  
• 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

  
  
• 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

  
  
• 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

  
  
• 14
  
  

  Continuous Random Variables

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

  
  
• 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

  
  
• 16
  
  

  The Gaussian CDF

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

  
  
• 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

  
  
• 18
  
  

  Conditioning one random variable on another

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

  
  
• 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

  
  
• 20
  
  

  Derived Distributions

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

  
  
• 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

  
  
• 22
  
  

  Applications of Covariance

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

  
  
• 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

  
  
• 24
  
  

  Markov and Chebychev Inequalities, Convergence In Probability

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

  
  
• 25
  
  

  The Weak Law of Large Numbers

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

  
  
• 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

  
  
• 27
  
  

  The Bernoulli Process

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

  
  
• 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

  
  
• 29
  
  
   

  
  
• 30