Let X1, X2, , Xn represent a random sample from a Rayleigh distribution with pdf a It can be shown that E(X2) 2 Icirc cedil Use this fact to construct an unbiased estimator of Icirc cedil based on Icirc pound Xi2 (and use rules of expected value to show that it is unbiased) b Estimate u from the following n 10 observations on vibratory stress of a turbine blade under specified conditions e r (29) x 0 16 88 10 23 4 59 6 66 13 68 14 23 19 87 940 6 5 10 95

Question: Let X1, X2, ... , Xn represent a random sample from a Rayleigh distribution with pdf a. It can be shown that E(X2) = 2Î¸.

Let X1, X2, ... , Xn represent a random sample from a Rayleigh with pdf

a. It can be shown that E(X2) = 2Î¸. Use this fact to construct an unbiased estimator of Î¸ based on Î£Xi2 (and use rules of expected value to show that it is unbiased).
b. Estimate u from the following n = 10 observations on vibratory stress of a turbine blade under specified conditions:

e-r/(29) x>0 16.88 10.23 4.59 6.66 13.68 14.23 19.87 940 6.5 10.95

Step by Step Solution

★★★★★

3.40 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Then implying tha... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

1172-M-S-P-E(1203).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, . . ., Xn be a random sample from a Rayleigh distribution with pdf Find the MLEs of . f(x) 0, otherwise

Let X1, X2,... , Xn represent a random sample from the Rayleigh distribution with density function given in Exercise 15. Determine a. The maximum likelihood estimator of u, and then calculate the...

Let X1,...,Xn be a random sample from a n(Î¼x, Ï2x), and let Y1,...,Ym be an independent random sample from a n(Î¼Y, Ï2Y). We are interested in testing H0:...

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...

Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf a. It can be shown that E(X2 ) 2 . Use this fact to construct an unbiased estimator of based on (and use rules...

15. Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf a. It can be shown that E(X2) 2u. Use this fact to construct an unbiased estimator of u based on and use...

Could you kindly solve the below question on probability and statistics below perspective Let X,, X2 ... Xn represent a random sample from a Rayleigh distribution with Pdf f ( 2 ; 0 ) = 2 - e - 2 2...

1) Let X1, X2, ...Xn are i.i.d random sample from a Rayleigh Distribution with PDF (30 Points) . 2 exp( f (ac; 0) 20 = 0, 0.w a) Show that X?, i = 1, 2, ..n has a gamma distribution, [(1, 20) (Hint:...

Let X1, X2, . . . . X, represent a random sample from a Rayleigh distribution with the following pdf. f ( x ; 0 ) = -e- X-x2/ (20) x > 0 (a) Determine the maximum likelihood estimator of 0. O ( Ex,...

"Stockholders of Dogs R Us Pet Supply expect a 13% rate of return on their stock. Management has historically been generating an ROE of 12.5% but now believes that the future ROE will be 12% for the...

(1) in 1-2 complete sentences, define the following literary terms. once you have done so, submit your work for grading. definitions for all terms and concepts can be found in your textbook. symbol ...

Gizelle has scheduled an appointment with her financial planner to begin preparations for her retirement in three years. Which of the following is among the first things the planner should do as they...

What are our products and services that we deliver to our customers?

Here are the IQ scores for the 15 first-grade girls from the study mentioned in Example 15.9. Assume that the data is a random sample from a normal distribution with mean and = 15, and assign to l...

If and are large, then the beta distribution can be approximated by the normal distribution using the beta mean and variance given. This is useful in case beta distribution software is unavailable....

Two political scientists wish to forecast the proportion of votes that a certain U.S. senator will earn in her upcoming reelection contest. The first political scientist assigns a Beta(3, 2) prior to...

943. Jeremy was watching the news, and one of the stories was about the suspected malicious practises occurring in Jeremy's favourite shopping mall. When he wanted to share the news to his friend, he...

Oregon Transportation Inc. (OTI) just signed a contract to purchase light rail cars from a manufacturer in Germany or 2,500.000. The purchase was made in June with payment due six months later in...

Sachin has asked his flat mate Jason for a $450 loan to cover a portion of his rent and utility costs. Sachin proposes repaying the loan with $375 from each of his next two financial aid...