Unformatted text preview: 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 handout # 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 setup 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).3 points to be equally likely....
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 Spring '09
 Covariance, Probability theory, Covariance and correlation, matlab homework

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