Resource Index

OCW Scholar

This resource index gives users access to most of the course resources in a single location.

Unit I: Probability Models and Discrete Random Variables

TITLEs LECTURE VIDEOs SLIDES TEXTBOOK READINGS RECITATIONS TUTORIALS HELP VIDEOS PROBLEM SETS
Probability Models and Axioms Lecture 1: Probability Models and Axioms1 Lecture 1: Probability Models and Axioms Slides (PDF) Sections 1.1–1.2

Recitation 1 Problems (PDF)

Recitation 1 Solutions (PDF)

 None

The Probability of the Difference of Two Events (00:05:55)

Geniuses and Chocolates (00:08:43)

Uniform Probabilities on a Square (00:09:17)

Problem Set 1 (PDF)

Problem Set 1 Solutions (PDF)
Conditioning and Bayes' Rule Lecture 2: Conditioning and Bayes' Rule2 Lecture 2: Conditioning and Bayes' Rule Slides (PDF)

Sections 1.3–1.4

Recitation 2 Problems (PDF)

Recitation 2 Solutions (PDF)

 None

A Coin Tossing Puzzle (00:08:11)

Conditional Probability Example (00:14:22)

The Monty Hall Problem (00:15:59) 		None
Independence Lecture 3: Independence Lecture 3: Independence Slides (PDF) Section 1.5

Recitation 3 Problems (PDF)

Recitation 3 Solutions (PDF)

Tutorial 1 Problems (PDF)

Tutorial 1 Solutions (PDF)

A Random Walker (00:05:52)

Communication over a Noisy Channel (00:19:53)

Network Reliability (00:17:24)

A Chess Tournament Problem (00:18:33)

Problem Set 2 (PDF)

Problem Set 2 Solutions (PDF)
Counting Lecture 4: Counting Lecture 4: Counting Slides (PDF) Section 1.6

Recitation 4 Problems (PDF)

Recitation 4 Solutions (PDF)

Tutorial 2 Problems (PDF)

Tutorial 2 Solutions (PDF)

Rooks on a Chessboard (00:18:28)

Hypergeometric Probabilities (00:05:49) 		None
Discrete Random Variables; Probability Mass Functions; Expectations Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations Slides (PDF) Sections 2.1–2.3

Recitation 5 Problems (PDF)

Recitation 5 Solutions (PDF)

Tutorial 2 Problems (PDF)

Tutorial 2 Solutions (PDF)

Tutorial 3 Problems (PDF)

Tutorial 3 Solutions (PDF)

Sampling People on Buses (00:11:56)

PMF of a Function of a Random Variable (00:15:26)

Problem Set 3 (PDF)

Problem Set 3 Solutions (PDF)
Discrete Random Variable Examples; Joint PMFs Lecture 6: Discrete Random Variable Examples; Joint PMFs Lecture 6: Discrete Random Variable Examples; Joint PMFs Slides (PDF) Sections 2.4–2.6

Recitation 6 Problems (PDF)

Recitation 6 Solutions (PDF)

Tutorial 3 Problems (PDF)

Tutorial 3 Solutions (PDF)

Flipping a Coin a Random Number of Times (00:08:43)

Joint Probability Mass Function (PMF) Drill 1 (00:17:37)

The Coupon Collector Problem (00:07:15) 		None
Multiple Discrete Random Variables Lecture 7: Multiple Discrete Random Variables Lecture 7: Multiple Discrete Random Variables Slides (PDF) Sections 2.6–2.7

Recitation 7 Problems (PDF)

Recitation 7 Solutions (PDF)

Tutorial 3 Problems (PDF)

Tutorial 3 Solutions (PDF)

 Joint Probability Mass Function (PMF) Drill 2 (00:13:45)

Problem Set 4 (PDF)

Problem Set 4 Solutions (PDF)

Quiz I

QUIZ SCOPE PREPARATION MATERIALS QUIZ AND SOLUTIONS
Quiz 1 covers
  • Lectures 1 through 7
  • Textbook Chapters 1 and 2
  • Recitations 1 through 7
  • Tutorials 1 through 3
  • Problem Sets 1 through 4

Quiz 1 Slides (PDF)

Quiz 1 Spring 2009 (PDF)
Quiz 1 Spring 2009 Solutions (PDF)

Quiz 1 Fall 2009 (PDF)
Quiz 1 Fall 2009 Solutions (PDF)

Recitation 10 Problems (PDF)
Recitation 10 Solutions (PDF)

Quiz 1 (PDF)

Quiz 1 Solutions (PDF)

Unit II: General Random Variables

TITLEs LECTURE VIDEOs SLIDES TEXTBOOK READINGS RECITATIONS TUTORIALS HELP VIDEOS PROBLEM SETS
Continuous Random Variables Lecture 8: Continuous Random Variables Lecture 8: Continuous Random Variables Slides (PDF) Sections 3.1–3.3

Recitation 8 Problems (PDF)

Recitation 8 Solutions (PDF)

Tutorial 4 Problems (PDF)

Tutorial 4 Solutions (PDF)

Calculating a Cumulative Distribution Function (CDF) (00:08:44)

A Mixed Distribution Example (00:13:25)

Mean and Variance of the Exponential (00:15:11)

Normal Probability Calculation (00:05:25) 		None

 
Multiple Continuous Random Variables Lecture 9: Multiple continuous Random Variables Lecture 9: Multiple Continuous Random Variables Slides (PDF) Sections 3.4–3.5

Recitation 9 Problems (PDF)

Recitation 9 Solutions (PDF)

Tutorial 4 Problems (PDF)

Tutorial 4 Solutions (PDF)

Uniform Probabilities on a Triangle (00:22:58)

Probability that Three Pieces Form a Triangle (00:12:30)

The Absent Minded Professor (00:13:09)

Problem Set 5 (PDF)

Problem Set 5 Solutions (PDF)
Continuous Bayes' Rule; Derived Distributions Lecture 10: Continuous Bayes' Rule; Derived Distributions Lecture 10: Continuous Bayes' Rule; Derived Distributions Slides (PDF) Sections 3.6 and 4.1

Recitation 11 Problems (PDF)

Recitation 11 Solutions (PDF)

Tutorial 5 Problems (PDF)

Tutorial 5 Solutions (PDF)

Inferring a Discrete Random Variable from a Continuous Measurement (00:18:37)

Inferring a Continuous Random Variable from a Discrete Measurement (00:11:35)

A Derived Distribution Example (00:09:30)

The Probability Distribution Function (PDF) of [X] (00:09:06)

Ambulance Travel Time (00:06:47) 		None
Derived Distributions; Convolution; Covariance and Correlation Lecture 11: Derived Distributions; Convolution; Covariance and Correlation Lecture 11: Derived Distributions; Convolution; Covariance and Correlation Slides (PDF) Sections 4.1–4.2

Recitation 12 Problems (PDF)

Recitation 12 Solutions (PDF)

Tutorial 6 Problems (PDF)

Tutorial 6 Solutions (PDF)

The Difference of Two Independent Exponential Random Variables (00:06:12)

The Sum of Discrete and Continuous Random Variables (00:05:37) 		None
Iterated Expectations; Sum of a Random Number of Random Variables Lecture 12: Iterated Expectations; Sum of a Random Number of Random variables Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables Slides (PDF) Sections 4.3 and 4.5

Recitation 13 Problems (PDF)

Recitation 13 Solutions (PDF)

Tutorial 6 Problems (PDF)

Tutorial 6 Solutions (PDF)

The Variance in the Stick Breaking Problem (00:11:30)

Widgets and Crates (00:10:06)

Using the Conditional Expectation and Variance (00:10:10)

A Random Number of Coin Flips (00:07:19)

A Coin with Random Bias (00:22:58)

Problem Set 6 (PDF)

Problem Set 6 Solutions (PDF)

Quiz 2

QUIZ SCOPE PREPARATION MATERIALS QUIZ AND SOLUTIONS
Quiz 2 covers
  • Lectures 1 through 12
  • Textbook Chapters 1 and 4
  • Recitations 1 through 13
  • Tutorials 1 through 6
  • Problem Sets 1 through 6

Quiz 2 Slides (PDF)

Quiz 2 Spring 2008 (PDF)
Quiz 2 Spring 2008 Solutions (PDF)

Quiz 2 Fall 2009 (PDF)
Quiz 2 Fall 2009 Solutions (PDF)

Quiz 2 (PDF)

Quiz 2 Solutions (PDF)

Unit III: Random Processes

TITLEs LECTURE VIDEOs SLIDES TEXTBOOK READINGS RECITATIONS TUTORIALS HELP VIDEOS PROBLEM SETS
Bernoulli Process Lecture 13: Bernoulli Process Lecture 13: Bernoulli Process Slides (PDF) Section 6.1

Recitation 14 Problems (PDF)

Recitation 14 Solutions (PDF)

Tutorial 7 Problems (PDF)

Tutorial 7 Solutions (PDF)

 Bernoulli Process Practice (00:08:22) None
Poisson Process - I Lecture 14: Poisson Process - I Lecture 14: Poisson Process - I Slides (PDF) Section 6.2

Recitation 15 Problems (PDF)

Recitation 15 Solutions (PDF)

Tutorial 7 Problems (PDF)

Tutorial 7 Solutions (PDF)

 Competing Exponentials (00:07:43) None
Poisson Process - II Lecture 15: Poisson Process - II Lecture 15: Poisson Process - II Slides (PDF) Section 6.2

Recitation 17 Problems (PDF)

Recitation 17 Solutions (PDF)

Tutorial 8 Problems (PDF)

Tutorial 8 Solutions (PDF)

 Random Incidence Under Erlang Arrivals (00:09:43)

Problem Set 7 (PDF)

Problem Set 7 Solutions (PDF)
Markov Chains - I Lecture 16: Markov Chains - I Lecture 16: Markov Chains - I Slides (PDF) Sections 7.1–7.2

Recitation 18 Problems (PDF)

Recitation 18 Solutions (PDF)

Tutorial 9 Problems (PDF)

Tutorial 9 Solutions (PDF)

Setting Up a Markov Chain (00:10:36)

Markov Chain Practice 1 (00:11:41) 		None
Markov Chains - II Lecture 17: Markov Chains - II Lecture 17: Markov Chains - II Slides (PDF) Section 7.3 None

Tutorial 9 Problems (PDF)

Tutorial 9 Solutions (PDF)

 None

Problem Set 8 (PDF)

Problem Set 8 Solutions (PDF)
Markov Chains - III Lecture 18: Markov Chains - III Lecture 18: Markov Chains - III Slides (PDF) Section 7.4

Recitation 19 Problems (PDF)

Recitation 19 Solutions (PDF)

Tutorial 10 Problems (PDF)

Tutorial 10 Solutions (PDF)

 Mean First Passage and Recurrence Times (00:09:27) None

Unit IV: Laws Of Large Numbers And Inference

TITLEs LECTURE VIDEOs SLIDES TEXTBOOK READINGS RECITATIONS TUTORIALS HELP VIDEOS PROBLEM SETS
Weak Law of Large Numbers Lecture 19: Weak Law of Large Numbers Lecture 19: Weak Law of Large Numbers Slides (PDF) Sections 5.1–5.3

Recitation 20 Problems (PDF)

Recitation 20 Solutions (PDF)

Tutorial 10 Problems (PDF)

Tutorial 10 Solutions (PDF)

Convergence in Probability and in the Mean Part 1 (00:13:37)

Convergence in Probability and in the Mean Part 2 (00:05:46)

Convergence in Probability Example (00:07:37)

Problem Set 9 (PDF)

Problem Set 9 Solutions (PDF)
Central Limit Theorem Lecture 20: Central Limit Theorem Lecture 20: Central Limit Theorem Slides (PDF) Section 6.2

Recitation 21 Problems (PDF)

Recitation 21 Solutions (PDF)

 None

Probabilty Bounds (00:10:46)

Using the Central Limit Theorem (00:11:25) 		None
Bayesian Statistical Inference - I Lecture 21: Bayesian Statistical Inference - I Lecture 21: Bayesian Statistical Inference - I Slides (PDF)   None None None None
Bayesian Statistical Inference - II Lecture 22: Bayesian Statistical Inference - II Lecture 22: Bayesian Statistical Inference - II Slides (PDF) Sections 8.3–8.4

Recitation 22 Problems (PDF)

Recitation 22 Solutions (PDF)

Tutorial 11 Problems (PDF)

Tutorial 11 Solutions (PDF)

Inferring a Parameter of Uniform Part 1 (00:24:52)

Inferring a Parameter of Uniform Part 2 (00:19:36)

An Inference Example (00:27:51)

Problem Set 10 (PDF)

Problem Set 10 Solutions (PDF)
Classical Statistical Inference - I Lecture 23 Classical Statistical Inference - I Lecture 23: Classical Statistical Inference - I Slides (PDF) Section 7.3

Recitation 23 Problems (PDF)

Recitation 23 Solutions (PDF)

Recitation 24 Problems (PDF)

Recitation 24 Solutions (PDF)

Tutorial 11 Problems (PDF)

Tutorial 11 Solutions (PDF)

 None None
Classical Inference - II Lecture 24: Classical Inference - II Lecture 24: Classical Inference - II Slides (PDF) Sections 9.2–9.3

Recitation 24 Problems (PDF)

Recitation 24 Solutions (PDF)

 None None None
Classical Inference - III Lecture 25: Classical Inference - III; Course Review Lecture 25: Classical Inference - III Slides (PDF) Section 9.4 None None None

Problem Set 11 (PDF)

Problem Set 11 Solutions (PDF)

Final Exam

FINAL EXAM SCOPE PREPARATION MATERIALS QUIZ AND SOLUTIONS
The Final Exam covers the entire course, however the emphasis is on the material not covered in Quiz 1 and Quiz 2.

Quiz Spring 2009 (PDF)
Quiz Spring 2009 Solutions (PDF)

Quiz Fall 2009 (PDF)
Quiz Fall 2009 Solutions (PDF)

Final Exam (PDF)

Final Exam Solutions (PDF)