Let $x_1,x_2,$dots,$x_n$ be a random sample from pdf$.$

$f_x(x$;$)=\{\begin{array}{ccc}\frac{1}{}{e}^{-\frac{1}{}},& x>0,& E(x)=\\ 0,& d.y.\text{V}\text{a}\text{r}& (x)={}^2\end{array}$

Assume that the statistics given below are the estimators for the parameter $.$

hat$({)}_1=\frac{x_1+x_2}{2},$hat$({)}_2=\frac{x_1+2x_2+x_3}{4},$hat$({)}_3=\frac{2}{n(n+1)}{\displaystyle \underset{i=1}{\overset{n}{}}}i{x}_1,$hat$({)}_4={\stackrel{}{x}}_n$

Examine the unbiasedness, consistency, and efficiency properties of these estimators.