Consider a random experiment of tossing a die and two random variables such that X =1{even} and X =1{w 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 {X = 1} and justify your estimator.