markscheme seems clear enough.
3 iid rvs, you should almost intuitively know the best unbiased estimator of the mean is the sample average, i.e.
$\bar{\mu} = \dfrac 1 3 (X_1+X_2+X_3)$
the variance of $\bar{\mu}$ is
$V[\bar{\mu}] = \dfrac 1 9 \left(\sigma^2 + \sigma^2 + \sigma^2\right) = \dfrac {\sigma^2}{3}$
$\dfrac 1 3 < \dfrac 3 8$
What isn't clear?
Hey bbear123.
Hint - You know E[Xn] = mu [from your first post] and if U is unbiased estimator for mu then E[U] = mu as well.
This should help summarize what you need to do to find the unknowns.
Hint - you will need two equations in two unknowns to get alpha and beta and I would recommend looking at the Variance operator to do so.