Please see the attached file for full problem description.
? A random sample of independent observations is taken from a Rayleigh distribution, whose density function is given by
for x> or equal to 0
0 if x<0
show that the maximum likelihood estimate is given by .
Using the result that deduce that is an unbiased estimator of and has variance . What reason would you give for supposing that the distribution of is approximately normally distributed for large n?
This shows how to make a judgment about the variance and unbiased estimator in a Rayleigh distribution.