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# Exam1_2 - f X Y x y = x 1 x> 1 0< y< x 1 zero...

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STAT 410 Spring 2008 Name _________________________ Exam 1 ( part 2 ) ( 4 points ) No credit will be given without supporting work. If the answer is a function, its support must be included. 1. (1) Let X and Y be two independent random variables, with probability density functions f X ( x ) and f Y ( y ) , respectively. ( ) ° ± ° ² ³ = otherwise 0 1 0 3 2 X x x x f ( ) ± ² ³ = otherwise 0 1 0 2 Y y y y f Find the p.d.f. f W ( w ) of W = X + Y. 2. (2) Let X and Y have the joint probability density function
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Unformatted text preview: f X , Y ( x , y ) = x 1 , x > 1, 0 < y < x 1 , zero elsewhere. a) Find f Y ( y ). b) Find f Y | X ( y | x ). c) Find E ( X ). d) Find E ( X | Y = y ). 3. (1) Let X and Y have the joint probability density function f X , Y ( x , y ) = x 1 , x > 1, 0 < y < x 1 , zero elsewhere. Let U = Y and V = Y / X. Find the joint probability density function of ( U, V ), f U , V ( u , v ). Sketch the support of ( U, V )....
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