1. (a) Explain what is meant by the sampling distribution of an estimator \(T\) of the population parameter \(\theta\).
   (b) Explain what you understand by the statement that \(T\) is a biased estimator of \(\theta\).

A population has mean \(\mu\) and variance \(\sigma ^ { 2 }\)
A random sample \(X _ { 1 } , X _ { 2 } , \ldots , X _ { 10 }\) is taken from this population.
(c) Calculate the bias of each of the following estimators of \(\mu\). $$\begin{aligned} & \hat { \mu } _ { 1 } = \frac { X _ { 3 } + X _ { 5 } + X _ { 7 } } { 3 }
& \hat { \mu } _ { 2 } = \frac { 5 X _ { 1 } + 2 X _ { 2 } + X _ { 9 } } { 6 }
& \hat { \mu } _ { 3 } = \frac { 3 X _ { 10 } - X _ { 1 } } { 3 } \end{aligned}$$ (d) Find the variance of each of these three estimators.
(e) State, giving a reason, which of these three estimators for \(\mu\) is

1. the best estimator,
2. the worst estimator.