Please use R programming to solve the question.

(a) Let Ui,1i3, be i.i.d. Uniform (0,1) random variables. Suppose that (X,Y) is a random vector such that X:=min{1i3Uii/3} and Y has Binomial(x,1/3) distribution given that X=x. Estimate E[XY] by generating 100 i.i.d. copies of (X,Y). (b) Estimate E(X6) based on 100 i.i.d. copies, to be generated by the composition method, of a random variable X having the following p.m.f.: P{X=j}=(j1)!e22j3+3j12j3,j=1,2