Question

1. (20 points) Let X1....X be a random sample from a uniform distribution over [0,0]. (a) (4 points) Find the maximum likelihood estimator (MLE) 0 MLE for 0. (b) (3 points) Is the MLE ONLE unbiased for 0? If yes, prove it: If not, construct an unbiased estimator 0, based on the MLE. (c) (4 points) Find the method of moment estimator (MME) OM ME for 8. (d) (3 points) Is the MME OMME tnbiased for 6? If yes, prove it: If not, construct an unbiased estimator 0, based on the MME. (e) (3 points) Compare two unbiased estimators in (b) and (d) in terms of relative efficiency. Which one is more efficient? (f) (3 points) Is the MLE OMLE Or MME OME a sufficient statistic for 0? If yes, prove it: If both not find a sufficient statistic for 0.

Answer 1

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