Question: Two random variables X and Y have a joint Gaussian PDF with X = 1, Y = -1, 2 = 1, 2 = 4 and

Two random variables X and Y have a joint Gaussian PDF with X = 1, Y = -1, 2 = 1, 2 = 4 and a correlation coefficient = 0.5 For this problem, you can use the formula on pages 12 and 14 of the slides from lecture 14. (a) Find E[X (Y - X)] (b) What is the correlation coefficient of Z = X + Y and W = 2X - Y? (You should get 1/28) (c) Find the conditional expected value of W given that Z = 1 (Ans: 20/7) (d) Find the conditional variance of W given that Z = 1 (Ans: 27/7) (e) What is the conditional probability that W < 3 given that Z = 1 (You should get a value close to 0.529)

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