# All of Statistics - Chapter 6 Solutions

## 1.

Since , the estimator is unbiased. Moreover, . By the bias-variance decomposition, the MSE is equal to .

## 2.

If is between and ,

Differentiating yields the PDF of between and as . Therefore,

It follows that the bias of this estimator is Moreover,

By the bias-variance decomposition, the MSE is .

*Remark*. is an unbiased estimator.

## 3.

Since , the estimator is unbiased. Moreover,

By the bias-variance decomposition, the MSE is equal to .