Originally Posted by

**noname** Hi

I've this question:

X1,...,Xn it's a sample from a binomial distribution b(n,a). Find the maximum likelihood estimator of a and the expected value of the estimator.

I can find the MLE

Ignoring the binomial coefficient i have

$\displaystyle

f(x_1,...,x_n|a)=a^{\sum_{1}^{n}x_i}(1-a)^{n^2-\sum_{1}^{n}x_i}

$

I take logs and differentiate to obtain:

$\displaystyle

\frac{d}{da}logf(x_1,...,x_n|a)=\frac{\sum_{1}^{n} x_i}{a}-\frac{n^2-\sum_{1}^{n}x_i}{1-a}

$

Upon equating to zero and solving i obtain that:

$\displaystyle

a=\frac{\sum_{1}^{n}x_i}{n^2}

$

Now i must find the expected value of a but I'm very confused on how to do this. Any hint?

Thanks