We have a r.v. ~
And I have worked out that the Cramer Rao Lower Bound for the var of any unbiased est of to be
Now, I'm given that
(in case there's any confusion, the sum is from i=1 to n, I'm not sure how to do that on LaTex)
How do I show that is a minimum variance unbiased estimator of ?
Your estimator looks like it is using n sets of 12 (that is a total of 12n Bernoulli trials). It is the sum of n (presumably independent) RVs ~Bin(12,theta)
(Other than the above you will find that the variance of your estimator is equal to the CRLB, it would also help if you simplify what is inside your brackets)
CB