Let X and Y be independent geometric distributions. U = min(X,Y), V = X - Y
(a) Show that U and V are independent
(b) Find the distribution of Z = X / (X+Y)
(c) Find the joint pdf of X and (X +Y)
Suppose the distribution of Y, conditional on X = x, is N(x, x^2), and marginal of X is U[0,1].
(a) Find E[Y], Var[Y], Cov(X, Y)
(b) Are the random variables U = Y / X and V = X independent?