solve the question below

Let ce (V3, 2). We generate random variables X1, X2, ... as follows. Suppose that the first person picks a point X1 randomly from [0, 1], i.e., X1 ~ U[0, 1]; for n = 1, 2, ..., given Xn, the (n+ 1)-th person picks a point Xn+1 randomly from [0, cX,], i.e., the conditional distribution of Xn+1 given Xn is U[0, cXn]. (a) Find E(X2). (b) Find E(Xn) for general n = 1, 2, .... Also find limn +% E(Xn). (c) Find the probability limit of Xn as n -> oo, i.e., find the value of constant C' such that Xn - Cas n - co. (d) Find E(X2). Does E(X_) converge to a finite value as n - oo