Consider a random experiment of tossing a die and two random variables such that X1 = 1{even} and X2 = 1 { 3} .

(a) Construct the sigma field generated by X = (X1, X2)'.

(b) Suppose that the dice is a fair die. Compute E (X2|X1).

(c) Now suppose that you do not know whether the die were fair or not but you have a sample of n iid observations of X1. Propose an estimator of = P {X1 = 1} and justify your estimator