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Variance and unbiased estimator

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Please see the attached file for full problem description.

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? 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?

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This shows how to make a judgment about the variance and unbiased estimator in a Rayleigh distribution.

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