Thread: minimum variance unbiased estimators

Show that the sample proportion (X/n) is a minimum variance unbiased estimator of the binomial parameter theta. The hint that is given is to treat (X/n) as the mean of a random sample of size n from a Bernoulli population with the parameter theta.

So, I know that I have to use the Cramer-Rao inequality. And I also know the distribution of Bernoulli, which is f(x; theta) = (theta^x)((1-theta)^(1-x)). I took the natural log of this and the partial derivative but I don't know what to do with the expected value of it. Can anyone help me?

You need to understand X and the sample of Xi's
It might be clearer if you use Y instead of X
The distribution of each Xi is



Next take the product of these, for your likelihood function and

let