1. [18 marks in total] Let Y1, . . . ,'Yn be data from a data model with probability mass function: p(y;='r) = 7W1 -Tr)1_y wherey=00rland0$1r5L a. [3 marks] Show that the mean and variance of the distribution are given by E(Y) = 7r and var(Y) = rr(l 1T). b. [2 marks] Find the method-of-moments estimator of 7r. Is the estimator unbiased? c. [4 marks] Find the mean squared error of the method-of-moments estimator of 1r, and hence show that the estimator is consistent. d. [4 marks] Suggest an estimator for var(Y). Is your estimator an unbiased estimator of var(Y)? If not, give an adjustment that makes it unbiased