# Math Help - Maximum Likelihood Estimator

1. ## Maximum Likelihood Estimator

Hi all,

I have been going through a practice paper for an exam I have on Friday and have found a question that I don't think we've been taught. Could anyone shed some light on the following question:

Let x1,x2,....,xnbe a random sample from a population whose probability density is given by

$f(x) = \theta x^ {\theta - 1}, 01$

Show that the maximum likelihood estimator of 1/q is -Sln x $_i$/n, and that this estimator is unbiased.
I'm not asking for the question to be solved, but if someone point me in the right direction, I'd be very grateful.

2. 1. $L(X_1,..X_n; \theta) = \prod f(x_i ; \theta)L(X_1,..X_2; \theta) = \prod f(x_i ; \theta)$
2. $l(\theta) = ln L(X_1,...,X_n ; \theta)$ (take the natural logarithm of the likelihood function)
3.Take the partial derivative of $l(\theta)$ (also called the score function) and set it to 0. Now, solve for theta hat.