please solve

Consider the univariate random variables X and Y with a joint density fX,Y (x, y) = ke4x e 7y , 0 < x < y < , 0, otherwise, where k > 0 is an unknown constant. (a) Evaluate k. (b) Write a simple R function for computing fX,Y (x, y). (c) Write down fY |X(y|x). Hence nd E(Y |X) and evaluate Var(E(Y |X)). (d) Find the covariance between X and Y . (e) Prove the law of total variance, i.e. Var(Y ) = E(Var(Y | X)) + Var(E(Y | X)).