Hello I am trying to check if the Method of Moments and Maximum Likelihood Estimators for parameter $\theta$ from a sample with population density $$f(x;\theta) = \frac 2 \theta x e^{\frac {-x^2}{\theta}} $$
for $$x \geq 0$, $\theta > 0$$ with $\theta$ being unknown.
Taking the first moment of...