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I have a problem in statistics that I don't quite know how to do:

"Generate a 1000-element data sample from the Rayleigh distribution. Graph the log-likelihood function $\ln L(\alpha; \vec{x})$ as a function of the parameter $\alpha$. From the graph determine the ML estimator and graphically find its standard deviation."

The Rayleigh distribution is given by:

$$f(x)=\frac{x}{\alpha^2} e^{-x^2 /2 \alpha^2} \ , \ \ \ x>0.$$

I have no idea how to graphically find the standard deviation of the estimator from the plot. I would appreciate suggestions on how to do it.

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