# Hw03 - STAT 410 Homework #3 (due Friday, February 8, by...

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STAT 410 Spring 2008 Homework #3 (due Friday, February 8, by 3:00 p.m.) 1. Suppose that the random variables X and Y have joint p.d.f. f ( x , y ) given by f ( x , y ) = C x 2 y , 0 < x < y , x + y < 2. a) Sketch the support of ( X , Y ). b) What must the value of C be so that f ( x , y ) is a valid joint p.d.f.? c) Find P ( X + Y < 1 ). 2. Suppose that the random variables X and Y have joint p.d.f. f ( x , y ) given by f ( x , y ) = 6 x 2 y , 0 < x < y , x + y < 2. a) Find the marginal probability density function for X. b) Find the marginal probability density function for Y. From the textbook: 2.1.6 Let f ( x , y ) = e x y , 0 < x < , 0 < y < , zero elsewhere, be the pdf of X and Y . Then if Z = X + Y , compute P ( Z 0 ), P ( Z 6 ), and, more generally, P ( Z z ), for 0 < z < . What is the pdf of Z ? 2.1.7 Let X and Y have the pdf f ( x , y ) = 1, 0 < x < 1, 0 < y < 1, zero elsewhere. Find the cdf and pdf of the product Z = X Y .

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2.1.9
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## This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

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Hw03 - STAT 410 Homework #3 (due Friday, February 8, by...

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