(8) If the random vector (X,Y) has the joint density f(x,y)=ex on 0<y<x<. Find the marginal density, mean and variance of X. Find those three things for Y. Are X and Y independent? What is the conditional density of Y given X=x ? What is E(YX) ? What is Var(YX) ? What is the conditional density of X given Y=y ? [Hint: Identify the marginal density of X, that of Y and the conditional density of Y given X=x as familiar densities] [10].