Let S = {1,2,3,4} and we consider the -algebra given by the power set 2. Let P defined on 2 be given by P(1) = P(2) = P(3) = P(4) = . i) Write down the -algebra generated by A = {1,2} given by (A). ii) Consider the random variables X and Y : R given by X (w) = w and Y = 4X. a) Compute E(X) and E(Y). b) Compute E[X|Y]. iii) Consider another random variable Z given by Compute E(X|Z). 1 X 3 Z = 1 X < 3.