410Hw03.pdf - STAT 410 Spring 2019 A Stepanov Homework#3(due Friday February 22 by 4:00 p.m Please include your name with your last name underlined your

410Hw03.pdf - STAT 410 Spring 2019 A Stepanov...

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STAT 410 Homework #3 (due Friday, February 22, by 4:00 p.m.) Spring 2019 A. Stepanov Please include your name ( with your last name underlined ) , your NetID, and your section number at the top of the first page. No credit will be given without supporting work. If the answer is a function, specify what kind of function it is ( pdf, pmf, cdf, or mgf ) , and its support must be included. 2. Let the joint probability density function of X and Y be defined by f ( x , y ) = 4 9 x y , 0 < y < 1, y < x < 3, zero otherwise. m) Find the probability distribution of W = X + Y. n) Let V = X Y. Find the joint probability density function of ( V, Y ) , f V, Y ( v , y ) . Sketch the support of ( V, Y ) . o) Find the probability distribution of

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Unformatted text preview: V = X Y. p) Let U = X / Y . Find the joint probability density function of ( X, U ) , f X, U ( x , u ) . Sketch the support of ( X, U ) . q) Find the probability distribution of U = X / Y . You are welcome to use a computer and/or calculator on any problem to evaluate any integral. For the supporting work, you should include the full integral (with the function and the bounds) and the answer. For example, x du u 2 = 3 3 x , 4 2 x x y dy dx = 32, 3 1 1 2 y dx dy x y = 2 9 ....
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• Spring '08
• AlexeiStepanov

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