Question: 4. The probability density function of the Rayleigh distribution is where is a positive-valued parameter. It is known that the mean and variance of

4. The probability density function of the Rayleigh distribution is

f(x) = ex/(20), x0,

where θ is a positive-valued parameter. It is known that the mean and variance of the Rayleigh distribution are

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Let X1, . . . ,Xn be a random sample from a Rayleigh distribution.

(a) Construct the method of moments estimator of θ. Is it unbiased?

(b) Construct a model-based estimator of the population variance. Is it unbiased?

f(x) = ex/(20), x0,

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