MATHEMATICAL STATISTICS QUESTION:

1) Suppose that X1, . . . , Xn form a random sample of size n from the uniform distribution on the interval [0, ] and thatand that Y(n) = max(X1, . . . , Xn).Suppose Y(n) is an estimator for parameter . Find MSE(Y(n)).

MSE stands for mean squared error.

2) Is the estimator in the previous problem an unbiased estimator for parameter ? If not, introduce a constant c, such that estimator cY(n)is an unbiased estimator for . Which estimator has the smaller MSE?