## Question

###### Two random variables, X and Y, havejoint probability density functionT<y<c+l; 0<a<l f (,y) = {6, otherwise1. Find cvalue. (5 pt) 2. What's the conditional p.d.f of Y given X = 3 , i.e;, fyiX-t (y) ? Don't forget the support of Y. (10 pt) 3. Find the conditional expectation E [YIx]: (10 pt) 4.Find thejoint p.d.f of Xand W = Y _ X.(10 pt) 5.Are V and W are independent? Justify your answer: (5 pt) 6.Find the cumulative distribution function of W. Which named distribution is th

Two random variables, X and Y, havejoint probability density function T<y<c+l; 0<a<l f (,y) = {6, otherwise 1. Find cvalue. (5 pt) 2. What's the conditional p.d.f of Y given X = 3 , i.e;, fyiX-t (y) ? Don't forget the support of Y. (10 pt) 3. Find the conditional expectation E [YIx]: (10 pt) 4.Find thejoint p.d.f of Xand W = Y _ X.(10 pt) 5.Are V and W are independent? Justify your answer: (5 pt) 6.Find the cumulative distribution function of W. Which named distribution is this? (10 pt)

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