# Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables

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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 (00:11:30) Jimmy Li
3 Widgets and Crates (00:10:06) 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 (00:10:10) Katie Szeto
3 A Random Number of Coin Flips (00:07:19) Katie Szeto
Bonus Problem A Coin with Random Bias (00:22:58) 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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