Pstat160AWinter 2009Homework #2Due Friday, January 23Submit also the Matlab homework assigned on the first week of classtogether with part 3.) of question 4 belowProblem 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 thatXandYare 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 sameprobability.a) Find the covariance and correlation ofX, Y.b) LetZ= 2X. Find the covariance and correlation ofZ, Ytwo ways: from the formula relatingXandZ, andby 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 other3 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. 91Use the indicator function trick.Problem 3.Problem 61, chapter 2, p.93. Do only
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Probability theory, Covariance and correlation, matlab homework