# Question

With reference to Example 10.4, find an unbiased estimator of β based on the smallest sample value (that is, on the first order statistic, Y1).

Example 10.4

If X1, X2, . . . , Xn constitute a random sample from a uniform population with α = 0, show that the largest sample value (that is, the nth order statistic, Yn) is a biased estimator of the parameter β. Also, modify this estimator of β to make it unbiased.

Example 10.4

If X1, X2, . . . , Xn constitute a random sample from a uniform population with α = 0, show that the largest sample value (that is, the nth order statistic, Yn) is a biased estimator of the parameter β. Also, modify this estimator of β to make it unbiased.

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