# 09_14 - STAT 410 Examples for Fall 2011 3 Consider two...

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STAT 410 Examples for 09/14/2011 Fall 2011 3. Consider two continuous random variables X and Y with joint p.d.f. f X, Y ( x , y ) = 60 x 2 y , x > 0, y > 0, x + y < 1, zero elsewhere. Consider W = X + Y. Find the p.d.f. of W, f W ( w ). - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Fact: Let X and Y be continuous random variables with joint p.d.f. ( ) y x f , . Then ( ) ( ) - = - + dx x w x f w f , Y X ( ) ( ) - = - + dy y y w f w f , Y X (convolution) Fact: Let X and Y be independent continuous random variables. Then ( ) ( ) ( ) - = - + dx x w f x f w f Y X Y X ( ) ( ) ( ) - = - + dy y f y w f w f Y X Y X - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1. a) Let X and Y be two independent Exponential random variables with mean 1. Find the probability distribution of Z = X + Y. That is, find ( ) z f Z = ( ) z f Y X + . 2.

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## This note was uploaded on 10/31/2011 for the course MATH 464 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.

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09_14 - STAT 410 Examples for Fall 2011 3 Consider two...

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