1. Suppose that X1, m, X is a random sample with the den sity of a single observation 4 fg($)=ai5, 05359 {a} Find the mean and variance of a single

Please help me to solve (e),(f),(g),(h),(i) and (j)! Thanks a lot!

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1. Suppose that X1, m, Xfl is a random sample with the den—sity of a single observation 4fg($)=fiai5, 05359 {a} Find the mean and variance of a single observation, Xi. {b} Find the maximum likelihood estimator, finne- (c) Find a such that P(c 5 at? 5 1) = 0.95 Hint: Think about the distribution of Xi/H and thenwhat that means for HMLE. {d} Use what you found in part (c) to derive a 95% oonfi:dence interval for 5'. {e} Find the CramervRao lower bound for the variance ofan estimator of I53 or explain why you cannot. (f) Is the MLE a biased estimator of 5'. {3} Is dMLE a sufficient statistic? (h) Find the method of moments litiinator for 5', finite(1} Find the variance and the MSE of dMLE. 1