where Xi, 1i, 0i, and Ui are mutually independent, Xi is a binary variable with Pr(Xi = 1) = 1/2, Ui Uniform[0, 1], and E[1i] = E[0i] = 0. (a) What is the treatment effect for unit i? (b) What is the average treatment effect (ATE)? (c) Calculate Pr(Di = 1|Xi = 1), Pr(Di = 1|Xi = 0), and Pr(Di = 1). (d) Calculate Pr(Xi = 1|Di = 1) and Pr(Xi = 1|Di = 0). (The Bayes' theorem, Pr(Xi = 1|Di = d) = Pr(Di=d|Xi=1) Pr(Xi=1) Pr(Di=d) , d {0, 1}, may be useful.) (e) What is the average treatment effect on the treated (ATT)