6.041SC | Fall 2013 | Undergraduate

# Probabilistic Systems Analysis and Applied Probability

## Unit II: General Random Variables

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This unit introduces continuous random variables and develops their properties in a manner that parallels the development for the discrete case. In addition, it covers a few more advanced topics such as the derivation of the distribution of a function of a random variable, covariance and correlation, and a more abstract view of the conditional expectation.

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

 Four variants of the Bayes’ rule Derived distributions

### 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 Inferring a Discrete Random Variable from a Continuous Measurement Jimmy Li
2 Inferring a Continuous Random Variable from a Discrete Measurement Jimmy Li
3 A Derived Distribution Example 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 The Probability Distribution Function (PDF) of [X] Jimmy Li
3 Ambulance Travel Time Kuang Xu

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### Lecture Topics

 Derived distributions for monotonic functions The PDF of the sum of independent random variables Covariance and correlation

### 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 The Difference of Two Independent Exponential Random Variables Kuang Xu

### 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
1 The Sum of Discrete and Continuous Random Variables Jagdish Ramakrishnan

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### Lecture Topics

 Conditional expectation Law of iterated expectations Law of total variance Sum of a random number of independent random variables Mean, variance

### 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 The Variance in the Stick Breaking Problem Jimmy Li
3 Widgets and Crates 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. There is also a bonus video solving a problem not represented in the tutorial problems.

#### Tutorial Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 Using the Conditional Expectation and Variance Katie Szeto
3 A Random Number of Coin Flips Katie Szeto
Bonus Problem A Coin with Random Bias Jimmy Li

### Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 6 covers Lectures 10, 11, and 12.

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### Lecture Topics

 Probability density functions Cumulative distribution functions Normal 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. 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 Calculating a Cumulative Distribution Function (CDF)

Jimmy Li
2 A Mixed Distribution Example Jagdish Ramakrishnan
3 Mean and Variance of the Exponential Jagdish Ramakrishnan

### 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
1 Normal Probability Calculation Jagdish Ramakrishnan

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### Lecture Topics

 PDF review Multiple random variables Conditioning Independence Examples Buffon’s needle Stick breaking

### 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
3 Uniform Probabilities on a Triangle Jimmy Li
4 Probability that Three Pieces Form a Triangle 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
3 The Absent Minded Professor Jimmy Li

### Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 5 covers Lectures 8 and 9.

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### Quiz Information

 Quiz 2 covers the following material Lectures 1 through 12 Textbook Chapters 1 and 4 Recitations 1 through 13 Tutorials 1 through 6 Problem Sets 1 through 6

### 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