# Question: With reference to Example 10 3 we showed on page 281

With reference to Example 10.3, we showed on page 281 that – 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, . . . , Xn constitute a random sample from the population given by

Show that is a biased estimator of ∂.

Example 10.3

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

Show that is a biased estimator of ∂.

## Answer to relevant Questions

With reference to Exercise 10.12, show that 2X – 1 is also an unbiased estimator of k, and find the efficiency of this estimator relative to the one of part (b) of Exercise 10.12 for (a) n = 2; (b) n = 3. Use Definition 10.5 to show that Y1, the first order statistic, is a consistent estimator of the parameter α of a uniform population with β = α + 1. Definition 10.5 The statistic is a consistent estimator of the ...If X1, X2, . . . , Xn constitute a random sample of size n from an exponential population, show that is a sufficient estimator of the parameter θ. Given a random sample of size n from a population that has the known mean µ and the finite variance σ2, show that Given a random sample of size n from a normal population with the known mean µ, find the maximum likelihood estimator for σ.Post your question