hw5solutions - AD Number_ Name_ Score_ IE 300 / GE 331 HW5...

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AD Number________ Name_________________________ Score________ IE 300 / GE 331 HW5 (10 pts) The joint probability density of (X,Y) is given by f(x,y)=c(xy+x+y+1) for 0<x<1 and -1<y<1 . a) Determine the constant c 1 = ?±²? + ² + ? + 1 ³´?´² 1 1 1 0 = 3c , ? = 1/3 . b) What is the probability P( (Y+1)/2<X<1-Y ) ? Line ² = 1 − ? and ² = ( ? + 1)/2 intersect at ( ² , ? ) = (2/3,1/3) . °± ( µ + 1)/2 < < 1 − µ ³ = · · ±²? + ² + ? + 1 ³ /3 ´²´? 1 −? ( ? +1)/2 1/3 0 + · · ±²? + ² + ? + 1 ³ /3 ´²´? 1 ( ? +1)/2 0 1 = 0.053 + 0.184 = 0.237 c)
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This note was uploaded on 03/16/2010 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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