# Question: With reference to Exercise 10 12 show that 2X 1

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.

(a) n = 2;

(b) n = 3.

## Answer to relevant Questions

Use the formula for the sampling distribution of 8 X on page 253 to show that for random samples of size n = 3 the median is an unbiased estimator of the parameter θ of a uniform population with α = θ – 12 and β = θ + ...With reference to Exercise 10.33, use Theorem 10.3 to show that Y1 – 1/n+1 is a consistent estimator of the parameter α. If X1 and X2 are independent random variables having binomial distributions with the parameters θ and n1 and θ and n2, show that X1 + X2 / n1 + n2 is a sufficient estimator of θ. Given a random sample of size n from a beta population with β = 1, use the method of moments to find a formula for estimating the parameter α. If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, find formulas for estimating its parameter α by using (a) The method of moments; (b) The method of maximum likelihood.Post your question