"Let $X_1, X_2, ..., X_n$ be a random sample with pdf $f(x; \theta)=\frac{1}{\theta^2}xe^{x\frac{1}{\theta}}$, with $x>0, E(X)=2\theta, V(X)=2\theta^2$ and $\theta > 0$ unknown. Find the maximum likelihood estimator, $\bar\theta$, for $\theta$."
I'm sort of confused by the mean and variance in this scenario. All the other samples that I had to find the MLE for did not have a mean & variance given, and I'd usually just use the log method. Is there any way I can leverage $E(X), V(X)$ here? Or do I have to at all?