Question: 15. Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf f(x; ) x

15. Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf f(x; )  

x

 e x2/(2) x 0

a. It can be shown that E(X2

)  2. Use this fact to construct an unbiased estimator of  based on X2 i (and use rules of expected value to show that it is unbiased).

b. Estimate  from the following n  10 observations on vibratory stress of a turbine blade under specified conditions:

6.88 10.23 4.59 6.66 13.68 14.23 19.87 9.40 6.51 10.95

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