Maximum Likelihood seems to be inexistant: f(x) = sqrt[theta/2*pi] e^{(-x^2)/theta} 1(x)_R, theta > 0

[maryyy]

Helllo

So I had a mini test, for my Inferential Statistics course.

We were given this function [imath] f(x) =\frac {\sqrt{\theta}}{\sqrt{2\pi}} e^{\frac{-x^2}{\theta}} \mathbb{1}(x)_\mathbb R , \theta > 0 [/imath]

And asked to determine the Maximum Likelihood Estimator of the given function. I used the method with the partial derivatives. In which the first partial derivative is equaled to 0 and then we extract the parameter. I had a negative value. Which is absurd since the parameter can't take a negative value.

So I feel like there might be a mistake in the given function, but I am not sure.

I would be grateful if anyone could try and comfort me or prove me wrong in my conclusions.

Thanks.

 

[BigBeachBanana]

I used the method with the partial derivatives. In which the first partial derivative is equaled to 0 and then we extract the parameter. I had a negative value. Which is absurd since the parameter can't take a negative value.

Please show your work.