Question: 2. (36 points) Suppose that Y.....Y, is a random sample from a population whose density is f(y0) = 30y y 20. for some parameter

2. (36 points) Suppose that Y.....Y, is a random sample from a population whose density is f(y0) = 30y y 20.

2. (36 points) Suppose that Y.....Y, is a random sample from a population whose density is f(y0) = 30y y 20. for some parameter > 0. As we showed in class, the maximum likelihood estimator of 0 is OMLE = min{Y.... Yn}. (a) Calculate B(0MLE), the bias of 0MLE. (b) Calculate MSE(@MLE), the mean-square error of MLE the standard error of OMLE (c) Calculate (d) Find a multiple of MLE that is an unbiased estimator of 0. Call it 0. (e) Find a multiple of Y that is an unbiased estimator of 0. Call it 02. (f) Compute Eff(0.02), the efficiency of 62 relative to , and determine which of these two unbiased estimators is preferable for the estimation of 0? Justify your answer.

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