The Rayleigh distribution has probability density function (a) It can be shown that E(X 2 ) 2 Icirc cedil Use this information to construct an unbiased estimator for Icirc cedil (b) Find the maximum likelihood estimator of Icirc cedil Compare your answer to part (a) (c) Use the invariance property of the maximum likelihood estimator to find the maximum likelihood estimator of the median of the Raleigh distribution X 20 f(x) Le 28 x 0, 0

Question: The Rayleigh distribution has probability density function (a) It can be shown that E(X 2 ) = 2Î¸. Use this information to construct an unbiased

The Rayleigh has probability density function

(a) It can be shown that E(X²) = 2Î¸. Use this information to construct an unbiased estimator for Î¸.

(b) Find the maximum likelihood estimator of Î¸. Compare your answer to part (a).

(c) Use the invariance property of the maximum likelihood estimator to find the maximum likelihood estimator of the median of the Raleigh distribution.

X -/20 f(x) = Le/28 x>0, 0

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