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hw5solutions - AD Number Name Score IE 300 GE 331 HW5(10...

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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 = ? ?? + ? + ? + 1 ???? 1 1 1 0 = 3c , ? = 1/3 . b) What is the probability P( (Y+1)/2<X<1-Y ) ? Line ? = 1 − ? and ? = ( ? + 1)/2 intersect at ( ? , ? ) = (2/3,1/3) . 𝑃 ( ? + 1)/2 < ? < 1 − ? = ?? + ? + ? + 1 /3 ???? 1 −? ( ? +1)/2 1/3 0 + ?? + ? + ? + 1 /3 ???? 1 ( ? +1)/2 0 1 = 0.053 + 0.184 = 0.237 c) What is the expectation of
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