. Let X1, X2, . . ., Xn represent a random sample from the Rayleigh distribution with density function given in Exercise 17. (a) Determine the maximum likelihood estimator of θ and then calculate the...

. Let X1, X2, . . ., Xn represent a random sample from the Rayleigh distribution with density

function given in Exercise 17.

(a) Determine the maximum likelihood estimator of θ and then calculate the estimate for the

vibratory stress data given in that exercise. Is this estimator the same as the unbiased

estimator suggested in Exercise 17?

(b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express

the median η in terms of θ.]