#4: Suppose that X1,... , X7n is an i.i.d. random sample drawn from a U[a, 1] uniform distribution, where 0a < 1. Suppose that you want to find an unbiased estimator, â, for a. (a) By definition, what relation must be satisfied for â to be an unbiased estimator of a (b) Use the first-order statistic to find an unbiased estimator of a. Recall that the first-order statistic has the p.d.f: п-1 g(yn)nf(yn) f(x)da Уп where f is the p.d.f. of each of the X;'s. (c) Find an alternative unbiased estimator â of a, which is still based on the random sample (hint: think of a common statistic we calculate from the random sample)

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