# Question: Show that the mean of a random sample of size

Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter θ.

## Answer to relevant Questions

Show that for the unbiased estimator of Example 10.4, n + 1 / n ∙ Yn, the Cramer-Rao inequality is not satisfied. If 1 and 2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean µ and the variance σ2, show that the variance of the unbiased estimator Is a minimum when ω = n1 / n1 + ...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 + ...Use the result of Example 8.4 on page 253 to show that for random samples of size n = 3 the median is a biased estimator of the parameter θ of an exponential population. If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + · · · + Xn is a sufficient estimator of the parameter θ.Post your question