Solve the problem:
Q1: Let X1, X2, X3......Xn represent a random sample from the Rayleigh distribution with destiny function given exercise 15. Determine:
a) The maximum likelihood estimator of theta and then calculate the estimate the vibratory stress data gven in the exercise. Is this estimator the same as the unbiased estimator suggested in Exercise 15.
b. The mle of the median of the vibratory stress distribution. (Hint: First express the median in the terms of theta.)
Q2: Let X1, X2, X3......Xn represent a random sample from the Rayleigh distribution with PDF
f(x;θ) - (X/θ)e-x2/2(θ) X>0
a) It can be shown that E(X2) = 2(θ). Use this fact to construct an unbiased estimator of theta based on (see document) (and use rules of expected value to show that it is unbiased).
b. Estimate (θ) from the following n = 10 observations on vibratory stress of a turbine blade under specified conditions:
16.88 10.23 4.49 6.66 13.68
14.23 19.87 9.40 6.51 10.95