# Question: Use the formula for the sampling distribution of 8 X

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 + 12.

## Answer to relevant Questions

Since the variances of the mean and the midrange are not affected if the same constant is added to each observation, we can determine these variances for random samples of size 3 from the uniform population By referring ...With reference to the uniform population of Example 10.4, use the definition of consistency to show that Yn, the nth order statistic, is a consistent estimator of the parameter β. Example 10.4 If X1, X2, . . . , Xn ...In reference to Exercise 10.43, is X1 + 2X2 / n1 + 2n2 a sufficient estimator of θ? If X1, X2, . . . , Xn constitute a random sample of size n from a population given by Find estimators for ∂ and θ by the method of moments. This distribution is sometimes referred to as the two-parameter exponential ...Given a random sample of size n from a Rayleigh population (see Exercise 6.20 on page 184), find an estimator for its parameter α by the method of maximum likelihood.Post your question