# Math425hw5 - SPRING 2009 MATH 425 Ralf Spatzier Homework 5...

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SPRING 2009 MATH 425 Ralf Spatzier Homework 5 for Wednesday, June 10 (1) The random variables X and Y have the joint density function f ( x,y ) = 12 x y (1 - x ) for ) < x < 1 , 0 < y < 1 and equal to 0 otherwise. (a) Are X and Y independent? (b) Find E [ X ]. (c) Find E [ Y ]. (d) Find V ar ( X ). (e) Find V ar ( X ). (2) Three points X 1 ,X 2 ,X 3 are selected a t random on a line L of length 1. What is the probability that X 2 lies between X 1 and X 3 ? (3) Let X and Y have joint density function f ( x,y ) = 1 x 2 y 2 x 1 ,y 1 . (a) Compute the joint density function of U = XY and V = X/Y . (b) What are the marginal densities of U and V ? (4) The gross daily sales at Amer’s is a normal random variable with mean \$2 , 200 and standard deviation \$230. What is the probability that (a) that the total gross sales over the next 2 days exceed \$5,000? (b) That the daily sales exceed \$2,000 in at least 2 of the next 3 days? (5) Suppose

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Math425hw5 - SPRING 2009 MATH 425 Ralf Spatzier Homework 5...

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