all of question 1

Exercise 1 Let X1, X2, ...Xn be i.i.d from the following discrete probability mass function: X l 2 P[X] % g 2 1-9 1-3 Let n1 represent the number of Is in the sample, n2 represent the number of 2s in the sample, etc. a) (1 pts) Find an expression for the Maximum Likelihood Estimator of 9, (3. A b) (1 pt) Find an expression for Bias of the MLE, Bias(6). c) (1 pt) Find an expression for the Method of Moments estimator of 3, 5". d) (0.5 pts) Find an expression for Bias of the MOM Estimator, Bias(). e) (1.5 pts) Find an expression for MSE of the MoM Estimator, M SEQ)