(20 pts) Let {Xi} be a random sample, where each X1- is independent and distributed according to p($):{ 1/2 iflgmg1 0 otherwise (a) Is Xi normally distributed? Why or why not? (b) What is the mean of X3? What is the variance of X3? (c) Let K; : (X1- X_1); for example Y2 : (X2 X1). What is E[Y;]'? Would your answer change if X:- and Xi_1 were not independent? Why or why not? (d) What is Var(Y,,;)? Could your answer change if Xi and X_1 were not independent? Why or why not