With reference to Example 10.3, we showed on page 281 that X̅ – 1 is an unbiased estimator of d, and in Exercise 10.8 the reader was asked to find another unbiased estimator of d based on the smallest sample value. Find the efficiency of the first of these two estimators relative to the second.

Example 10.3

If X₁, X₂, . . . , X_n constitute a random sample from the population given by

Show that X̅ is a biased estimator of ∂.

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[e-(x-5) for x > δ elsewhere