# Question: Show that the sample proportion X n is a minimum variance

Show that the sample proportion X/n is a minimum variance unbiased estimator of the binomial parameter θ.

## Answer to relevant Questions

Show that the mean of a random sample of size n is a minimum variance unbiased estimator of the parameter λ of a Poisson population. Rework Example 10.5 using the alternative formula for the information given in Exercise 10.19. Example 10.5 Show that is a minimum variance unbiased estimator of the mean µ of a normal population. Verify the result given for var(n + 1 / n ∙ Yn) in Example 10.6. 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. After referring to Example 10.4, is the nth order statistic, Yn, a sufficient estimator of the parameter β?Post your question