(→Problem 1: Coupon Collector) |
(→Problem 2: Minimum of Exponentials) |
||
| Line 6: | Line 6: | ||
== Problem 2: Minimum of Exponentials == | == Problem 2: Minimum of Exponentials == | ||
| + | *(a) <math>X_1</math> is an exponential random variable with parameter <math>\lambda_1</math>, and <math>X_2</math> with <math>\lambda_2</math>. Let <math>Y = \min(X_1,X_2)</math>. What is the PDF of <math>Y</math>? Is <math>Y</math> one of the common random variables? | ||
| + | *(b) | ||
== Problem 3: Random Chord == | == Problem 3: Random Chord == | ||
== Problem 4: Fire Station == | == Problem 4: Fire Station == | ||
Revision as of 06:52, 30 September 2008
Contents
Instructions
Homework 5 can be downloaded here on the ECE 302 course website.
Problem 1: Coupon Collector
Each brand of candy bar has one coupon in it. There are $ n $ different coupons in total; getting at least one coupon of each type entitles you to a prize. Each candy bar you eat can have any one of the coupons in it, with all being equally likely. Let $ X $ be the (random) number of candy bars you eat before you have all coupons. What are the mean and variance of $ X $?
Problem 2: Minimum of Exponentials
- (a) $ X_1 $ is an exponential random variable with parameter $ \lambda_1 $, and $ X_2 $ with $ \lambda_2 $. Let $ Y = \min(X_1,X_2) $. What is the PDF of $ Y $? Is $ Y $ one of the common random variables?
- (b)
