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Unformatted text preview: E120 Homework 5 Due 08/05/2010 Problem 1: A die is rolled twice. Let X equal the sum of the outcomes, and let Y equal the first outcome minus the second. 1. Are X and Y independent random variables? 2. Compute Cov(X,Y). 3. What is the lesson to be learned here? Problem 2: You are playing a normal game of roulette. Let X denote the winnings when placing an Even bet (you win $1 if the ball lands in one of the 2, 4, ..., 36 pockets). Let Y denote the winnings when placing an Odd bet. Let Z denote the winnings when placing a 00 bet (you win $35 if the ball land in the 00 pocket). Let W denote the winnings when placing a 1 bet (you win $35 if the ball land in the 1 pocket). 1. Find Cov(X,Y). 2. Find Cov(X,Z). 3. Find Cov(X,W). 4. Find Cov(Y,W). Problem 3: This exercise is to get you (re)-acquainted with basic matrix / vector multiplication. Note that you can use software like Matlab, Scilab (free), Octave (free), etc. to check your work....
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This note was uploaded on 08/15/2011 for the course ENGR 120 taught by Professor Alder during the Summer '11 term at Berkeley.
- Summer '11