the continuous random variable X and Y have a bivariate probability desnsity function fXY(x,y)= 2,where0<x+y<1 , x>0 ,y>0 and 0 o/w. a) show that the marginal distribution of Y is a beta distribution with probability density function i.e., Y-Beta(1,2).
b)-show that the conditional distribution of X given Y=y, is a uniform distribution with probability density function i.e.X/Y= y-U(0,1-y) .
c)- show that the conditional expectation of X given Y=y is E(X/Y=y)=1-y/2,and obtain the conditional varriance of Xgiven Y=y.
d)- verify in this case that Var(X)= E[(Var(X/Y=y)]+Var[E(X/Y=y)].