Question: Let X and Y have a joint probability density function f X , Y ( x , y ) = C x y e x

Let X and Y have a joint probability density functionfX,Y(x,y)=Cxyexy for 1<x<2,y>0, where C > 0 is an appropriate constant you will identify in part a.

a) Find the marginal probability density function of X.

b) Find the marginal probability density function of Y.

c) Find the conditional probability density function of Y given X=x(1,2).

d) Are X and Y independent? Please briefly explain your answer.

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