Let $X_1, X_2, ..., X_n$ be a random sample from a distribution who's PDF is given by $f(x; \theta)=(\theta+1)x^{\theta} $ for $0 \leq x \leq 1$ or $0$ otherwise.
Find the method-of-moments estimator for $\theta$.
So I have done the following:
$\mathbb{E}(X)=\int_{-\infty}^{\infty} xf(x) dx = (\theta +1)\int_{0}^{1}x^{\theta+1}dx=\frac{\theta +1}{\theta+2}$
I am unsure now how to equate this to $\bar{X}$
It's like Beck says. $\theta +1=\bar X (\theta+2) \Leftrightarrow \theta=\frac{2\bar X -1}{1-\bar X}$