the expected value of the MLE;

Y ~ gamma(2, θ), so E[Yi] = 2θ

E(MLE(θ))

= E(sum(Yi)/2n)

= (1/2n)sum(E[Yi])

= 2θn/2n

= θ; (so the MLE is unbiased)

similarly, var[Yi] = 2θ^2

var(MLE(θ))

= var(sum(Yi)/2n)

= (1/4n^2)sum(var(Yi)); (via independence)

= n2θ^2 / 4n^2

= θ^2 / 2n

for a hint on c, consider a 2 standard deviation bound on the estimator (you now have an estimate of θ - 63 - and the standard deviation of the estimator for any true θ and n). think in terms of a confidence interval.