a$)$ A random variable $Y,$ which is related to the angle $$ at which electrons are emitted

in $-$meson decay, obeys a distribution with the probability density function

$f(y|)=\frac{1+y}{2},-1y1$ and $-11.$

A random sample of experimental measurements $Y_1,Y_2,$dots.,$Y_n$ is collected and the

following method of moments estimator $T$ for the parameter $$ is considered,

where $T=\frac{3Y_1+3Y_2+\text{d}\text{o}\text{t}\text{s}\text{.}\text{.}+3Y_n}{n}.$

$($i$)$ Determine whether $T$ is an unbiased estimator of the parameter $.$

Show all your working.

$($ii$)$ Determine whether $T$ is a consistent estimator of the parameter $.$

Show all your working.

$($iii$)$ Examine whether a fully efficient estimator of the parameter $$ could

be found and give your conclusion.