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Unformatted text preview: ORIE 3500/5500 Engineering Probability and Statistics II Fall 2010 Assignment 4 Problem 1 The joint pmf of X and Y is given by p X,Y ( i,j ) = 1 3 n- 2 for 1 i,j n, | i- j | 1 , where a positive integer n 4 is a parameter. ( a ) Verify that this is a legitimate joint pmf. ( b ) Compute the marginal probability mass functions. Are X and Y independent? Problem 2 Let the joint density of X and Y be given by f X,Y ( x,y ) = xe- xy if 0 < x < 1 , y > . ( a ) Can you say whether X and Y are independent without comput- ing the marginal densities? ( b ) Now compute the marginal densities and verify your answer to part ( a ). Problem 3 Let X 1 ,...,X n be independent random variables, each having the standard mean 1 exponential distribution. ( a ) Let M =minimum( X 1 ,...,X n ). Show that the cdf of M is given by F M ( x ) = 1- e- nx , x > . Can you name this random variable? ( b ) Compute the cdf and the pdf of M 1 =maximum( X 1 ,...,X n )....
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This note was uploaded on 11/11/2010 for the course ORIE 3500 at Cornell University (Engineering School).