1. The continuous random variable \(X\) is uniformly distributed over the interval \([ 0,4 \beta ]\), where \(\beta\) is an unknown constant.

Three independent observations, \(X _ { 1 } , X _ { 2 }\) and \(X _ { 3 }\), are taken of \(X\) and the following estimators for \(\beta\) are proposed $$\begin{aligned} & A = \frac { X _ { 1 } + X _ { 2 } } { 2 }
& B = \frac { X _ { 1 } + 2 X _ { 2 } + 3 X _ { 3 } } { 8 }
& C = \frac { X _ { 1 } + 2 X _ { 2 } - X _ { 3 } } { 8 } \end{aligned}$$

1. Calculate the bias of \(A\), the bias of \(B\) and the bias of \(C\)
2. By calculating the variances, explain which of \(B\) or \(C\) is the better estimator for \(\beta\)
3. Find an unbiased estimator for \(\beta\)