6.041SC | Fall 2013 | Undergraduate

# Probabilistic Systems Analysis and Applied Probability

## Unit I: Probability Models And Discrete Random Variables

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This unit covers the basic framework of probability theory: probabilistic models, conditional probabilities, independence, the Bayes’ rule, and counting methods. In addition, it introduces discrete random variables and the concept of the Probability Mass Function (PMF) used to describe the probability distribution of one or several random variables. Finally, it defines the concepts of expectation and variance, and their basic properties.

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

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### Lecture Topics

 Probability as a mathematical framework for reasoning about uncertainty Probabilistic models Sample space Probability law Axioms of probability Simple examples

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Three of the problems have an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
1 The Probability of the Difference of Two Events Kuang Xu
2 Geniuses and Chocolates Katie Szeto
4 Uniform Probabilities on a Square Jimmy Li

### Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 1 covers Lecture 1.

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### Lecture Topics

 Conditional probability Three important tools Multiplication rule Total probability theorem Bayes’ rule

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Three of the problems have an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
1 A Coin Tossing Puzzle Kuang Xu
2 Conditional Probability Example Katie Szeto
4 The Monty Hall Problem Jimmy Li

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### Lecture Topics

 Independence of two events Independence of a collection of events

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Two of the problems have an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 A Random Walker Kuang Xu
3 Communication over a Noisy Channel Jimmy Li

### Tutorial Problems and Tutorial Help Videos

Review the tutorial problems in the PDF file below and try to solve them on your own. Two of the problems have an accompanying video where a teaching assistant solves the same problem.

#### Tutorial Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 Network Reliability Kuang Xu
3 A Chess Tournament Problem Katie Szeto

### Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 2 covers Lectures 2 and 3.

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### Lecture Topics

 Principles of Counting Examples of Counting Permutations Combinations Partitions Binomial Probabilities

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Two of the problems have an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 Rooks on a Chessboard Katie Szeto
3 Hypergeometric Probabilities Kuang Xu

### Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own. Check your answers when you’re done.

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### Lecture Topics

 Random Variables Probability of Mass Function (PMF) Expectation Variance

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
3 Sampling People on Buses Jimmy Li

### Tutorial Problems and Tutorial Help Videos

Review the tutorial problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

#### Tutorial Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 PMF of a Function of a Random Variable Katie Szeto

### Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 3 covers Lectures 4 and 5.

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### Lecture Topics

 Review: PMF, expectation, variance Conditional PMF Geometric PMF Total expectation theorem Joint PMF of two random variables

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Two of the problems have an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
1 Flipping a Coin a Random Number of Times Kuang Xu
2 Joint Probability Mass Function (PMF) Drill 1 Katie Szeto

### Tutorial Problems and Tutorial Help Videos

Review the tutorial problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

#### Tutorial Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 The Coupon Collector Problem Kuang Xu

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### Lecture Topics

 Multiple random variables Joint PMF Conditioning Independence More on expectations Binomial distribution revisited A hat problem

### Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

#### Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 Joint Probability Mass Function (PMF) Drill 2 Katie Szeto

### Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

### Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 4 covers Lectures 6 and 7.

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### Quiz Information

 Quiz 1 covers the following material Lectures 1 through 7 Textbook Chapters 1 and 2 Recitations 1 through 7 Tutorials 1 through 3 Problem Sets 1 through 4

### Quiz and Solutions

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## Course Info

Fall 2013
##### Learning Resource Types
Lecture Videos
Recitation Videos
Problem Sets with Solutions
Exams with Solutions