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Rayleigh distribution

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A RV X, has a Rayleigh distribution if pdf takes the form fx(x) = x/theta (exp(-x^2/2theta)) where x>0 and theta is positive parameter. We know that E(X) = (theta pie/2) ^1/2, E(X^2) = 2 theta.

If the method of moments estimator is such that theta = (2/pie)^1/2 X and maximum likelihood estimator is 1/2n (Sum xi)^2 , how does one find the bias of the method of moment estimator and also show that the maxmum likelihood estimator is unbiased for theta

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The solution describes the determination of the moments of a Rayleigh distribution.

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