3. Consider a population described by a Uniform(a, a +1) distribution. (a) Find the PDF of X(1), the first order statistic. (b) Find E[a +1 – X(1)] directly (that is, without finding E[X (1)] first). (c) Use your answer to part (b) to find E[X(1)] (d) Is X(1) an unbiased estimator of a, an asymptotically unbiased estimator of a, or neither? If you determine that X(1) is not an unbiased estimator of a, construct an unbiased estimator of a based on X(1). (e) Find E ?(a +1 – X (1))2] directly and use it to find Var?a +1- X(1)] and thus to find Var(X (1)) (f) Use your answer from part (e) to find the variance of the unbiased estimator you found in part (d). Is this unbiased estimator consistent?