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MATHEMATICAL STATISTICS QUESTION: 1) Suppose that X1, . . . , Xn form a random sample of size n from the uniform distribution on the
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?
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