I would like to know:
Is $\beta$ a MLE?
If yes what is the mean of it: $E(\beta)=$?
given:
$x$ is a random variable
$f(x)=\sqrt{\frac{2}{\pi \theta^2}}\exp \left(-\frac{x^2}{2\theta^2}\right)$ with $\theta,x>0$
I got $\beta = \sqrt{\sum x_i^2/n}$
Doing the likelihood function and the first derivative however when I check the 2nd derivative it was not evident to be negative.
If anyone could help I would appreciate a lot!