View the step-by-step solution to:

# Consider a large population which has true mean and true standard deviation .

2. Consider a large population which has true mean μ and true standard deviation  . We take a sample of size 3 from this population, thinking of the sample as the RVs X1,X2,X3  where Xi  can be considered iid. We are interested in estimating μ .

(a) Consider the estimator μ1 = X1 + X2 − X3 . Is this estimator unbiased? Calculate the bias.

(b) Find the variance of μ1 .

(c) When estimating μ , explain why someone would prefer the estimator ¯X = (X1+X2+X3)/3 over μ1 .

(d) Now consider the estimator μ2 = (X1+X2+X3)/2 . Is this estimator unbiased? Calculate the bias.

(e) Compute the MSE for μ2 .

### Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

### -

Educational Resources
• ### -

Study Documents

Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

Browse Documents