The question says:
Let $X_1, X_2, ..., X_n$ be a random sample (I.I.D.) from the PDF:
$$ f(x,\theta) = \frac{1}{\theta (1-x)^2} e^{\frac{-x}{\theta (1-x)}} $$
for $0<x<1$, $\theta>0$.
Find the maximum likelihood estimator of $\theta$. Is this the same as the method of moments estimator?
So, I have solved the first part, I've got:
$$ \theta = \frac{\sum_{i=1}^{n} \frac{x}{1-x}} {n}$$
But, for the second part (method of moments), I'm trying to solve the $E(X)$ first ($\int_{0}^{1} x f(x,\theta) \ dx$), and I'm using Maple but it seems that it does not have a definite answer!
Any idea how to solve for $E(X)$?
Thanks.