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Unformatted text preview: (b) What value of p maximizes your answer in (a)? Problem 5. Suppose X and Y are random variables satisfying EX = EY and EX 2 = EY 2 < . Show that Cov( X-Y,X + Y ) = 0. The following problems are optional for students enrolled in 360, required for students enrolled in 560. Problem 6. Prove that if EX = Var X = 0, then P [ X = 0] = 1. Hint: rst, let a > and prove P [ | X | a ] = 0 . Then, explain why this fact means P [ X = 0] = 1 . Problem 7. Let X 1 ,...,X n be independent random variables uniformly distributed on [0 , 1]. Let Y = max( X 1 ,...,X n ). (a) Find the cdf F Y of Y . (b) Find EY ....
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- Fall '07