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160a09_hw2

160a09_hw2 - Pstat160A Homework#2 Due Friday January 23...

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Pstat160A Winter 2009 Homework #2 Due Friday, January 23 Submit also the Matlab homework assigned on the first week of class together with part 3.) of question 4 below Problem 1. For this problem, you need to read first about covariance, see hand-out # 1. A judicious use of the symmetry let you save a lot calculations. 1) Let ( X, Y ) have joint pdf such as each of the 4 points ( - 1 , 0) , (1 , 0) , (0 , - 1) , (0 , 1) have the same probability. Show that X and Y are uncorrelated, but are not independent. What is the issue here? 2) Let now ( X, Y ) have joint pdf such as each of the 5 points ( - 1 , - 1) , (0 , - 1) , (0 , 0) , (0 , 1) , (1 , 1) have the same probability. a) Find the covariance and correlation of X, Y . b) Let Z = 2 X . Find the covariance and correlation of Z, Y two ways: from the formula relating X and Z , and by computing it from their joint pdf. c) Back in the set-up of a), but this time let the points (0 , - 1) and (0 , 1) have each probability 1/3, and the other 3 points to be equally likely. Do as in a) and explain the difference with the result found in a). Problem 2. Problem 45, chapter 2, p. 91 Use the indicator function trick. Problem 3. Problem 61, chapter 2, p.93. Do only
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