Probabilistic Systems Analysis and Applied Probability

Resource Index

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 Geniuses and Chocolates Uniform Probabilities on a Square	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 Conditional Probability Example The Monty Hall Problem	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 Communication over a Noisy Channel Network Reliability A Chess Tournament Problem	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 Hypergeometric Probabilities	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 PMF of a Function of a Random Variable	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 Joint Probability Mass Function (PMF) Drill 1 The Coupon Collector Problem	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	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) A Mixed Distribution Example Mean and Variance of the Exponential Normal Probability Calculation	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 Probability that Three Pieces Form a Triangle The Absent Minded Professor	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 Inferring a Continuous Random Variable from a Discrete Measurement A Derived Distribution Example The Probability Distribution Function (PDF) of [X] Ambulance Travel Time	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 The Sum of Discrete and Continuous Random Variables	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 Widgets and Crates Using the Conditional Expectation and Variance A Random Number of Coin Flips A Coin with Random Bias	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	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	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	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 Markov Chain Practice 1	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	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 Convergence in Probability and in the Mean Part 2 Convergence in Probability Example	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 Using the Central Limit Theorem	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 Inferring a Parameter of Uniform Part 2 An Inference Example	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)