$$ $$ [2] $$ $$ 1. Let sx_{1}, X_(2), X_{3}$ and $x_{4}$ be a random sample from a Normal $\left(\mu, \sigma^{2} ight)$ population. Let \begin{aligned What \mu} _1} &=\frac{2}{10) x_{1}+\frac{3}{10) X_{2}+\frac{3} [10) X_{3}+\frac{410) x_{4} What[\mu)_[2] &=\frac{2}10) x_{1}+\frac{6) (10) X_{2}+\frac{2}[10] X_[3] W What\mu] [3] 8=\frac{3}{10) x_{1}+\frac{4}{10) X_{2}+\frac{3} (10) X_[3] end{aligned a) Find the mean squared error of SVhat{\mu}_{1}, What\mu}_{2}$ and $\hat[\mu}_{3}$ as estimators of $\mus. b) Find the relative efficiency of shat{\mu}_{2}$ with respect to Shat( \m)_[3$. What does this tell us about these estimators? [31 c) Which of the three estimators is the best estimator of $\mus. State a reason for your answer. 2. Let $x_{1}$ and $X_{2}$ be a random sample from a population with probability density function f(x; \theta)=\left\{\begin{array}{cc) 2 x \theta [2] & B