I am asked to calculate a confidence interval for a large sample based on a Rayleigh Distribtion: f_X(x;theta) = ((x^2)/(theta^2))exp((-x^2)/(2*theta^2)), x>=0, and theta>=0. I have found the maximum likelihood estimator for this distribution, but I am having difficulty finding the Fisher Information for the distribution. As soon as I have that figured out, I will have all I need to solve the problem.
Any ideas would be great. Thanks in advance.