Hi, I'm trying to solve the following problem:

Let Y1, Y2, ..., Yn denote a random sample from the probability density function

$\displaystyle

f(y|\theta)={(\theta + 1)}{y}^{\theta} $, for $\displaystyle 0 < y < 1, \theta > -1,$

and 0 elsewhere.

Find the MLE for $\displaystyle \theta$. Compare the answer to the method-of-moments answer: [2(Y bar) -1]/[1-(Y bar)

Sorry for that last part. Y bar means Y with the line on top.

I tried to do this by taking the lns of each term after multiplying the fy's, taking the derivative with respect to theta, and equating to zero but I end up with - (ln y + 1). Is this possible? I figure it's not since it asks to compare to the M.O.M. answer which seems totally different...

Any ideas?