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== 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? | *(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) | + | *(b) Use induction to show that the minimum of <math>n</math> exponential random variables with parameter 1 is an exponential random variable with paramter <math>n</math>. |
== Problem 3: Random Chord == | == Problem 3: Random Chord == | ||
== Problem 4: Fire Station == | == Problem 4: Fire Station == | ||
Revision as of 06:53, 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) Use induction to show that the minimum of $ n $ exponential random variables with parameter 1 is an exponential random variable with paramter $ n $.
