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Unformatted text preview: X . (c) Find P ( X > Y ). 4. X and Y have joint probability density function f X,Y ( x,y ) = ± x (1 + 3 y 2 ) / 4 , < x < 2 , < y < 1; , otherwise . Are X and Y independent? (e.g., check if f X,Y ( x,y ) = f X ( x ) · f Y ( y ).) 2 SIEO 3600, Assignment #5 5. The joint density of X and Y is given by f X,Y ( x,y ) = ( xexy , x > ,y > , , otherwise. (a) Compute the density of X . (b) Compute the density of Y . (c) Are X and Y independent? 6. Let X 1 ,X 2 ,...,X n be independent random variables, each having density f X ( x ) = ( 1 , ≤ x ≤ 1 , otherwise . Let M = max { X 1 ,X 2 ,...,X n } . Show that the distribution function of M , F M ( · ), is given by F M ( x ) = x n , ≤ x ≤ 1 What is the probability density function of M ?...
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This note was uploaded on 10/03/2011 for the course SIEO W3600 taught by Professor Yunanliu during the Spring '10 term at Columbia.
 Spring '10
 YUNANLIU

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