Suppose that X1, , Xn form a random sample from the exponential distribution with parameter Let the prior distribution of be improper with p d f 1 for 0 Find the posterior distribution of and show that the posterior mean of is 1 Xn

Question: Suppose that X1, . . . , Xn form a random sample from the exponential distribution with parameter . Let the prior distribution of

Suppose that X1, . . . , Xn form a random sample from the exponential with parameter θ. Let the prior of θ be improper with “p.d.f.” 1/θ for θ > 0. Find the posterior of θ and show that the posterior mean of θ is 1/Xn.

Step by Step Solution

★★★★★

3.32 Rating (176 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The posterior pdf is proportional to the likelihood n e... 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)

602-M-S-P-E (895).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

This question refers to information from the problem # 1, page 109, under Problems and Applications, chapter 5, in the textbook. Which of the following is true? A. The demand for subway rides in the...

A function y = f(x) is defined as follows: y = f(x) 1.0 1.025 1.049 1.072 Compute the values of dyldx and vidr at x =1.05. X 1.0 1.05 1.10 1.15 X 1.20 1.25 1.30 y = f(x) 1.095 1.118 1.140

Let X have the exponential distribution with parameter . Prove that the median absolute deviation of X is smaller than one-half of the IQR. (You can do this without actually calculating the median...

Suppose that X1, . . . , Xn form a random sample from an exponential distribution for which the value of the parameter is unknown ( > 0). Let () denote the prior p.d.f. of , and let denote the Bayes...

Suppose that X1, . . . , Xn form a random sample from an exponential distribution for which the value of the parameter is unknown ( > 0) and must be estimated by using the squared error loss...

Suppose that X1, . . . , Xn form a random sample from the exponential distribution with unknown parameter , and suppose that it is desired to test the following hypotheses: H0: 1/2, H1:

Suppose that X1, . . . , Xn form a random sample from the exponential distribution with mean . Let Xn be the sample average. Find a variance stabilizing transformation for Xn.

Suppose that X1, . . . , Xn form a random sample from an exponential distribution for which the value of the parameter is unknown. Determine the M.L.E. of the median of the distribution.

Suppose that X1, . . . , Xn form a random sample from the exponential distribution with parameter . Show that 2 has the 2 distribution with 2n degrees of freedom.

Suppose that X1, . . . , Xn form a random sample from an exponential distribution with parameter . Explain how to use the parametric bootstrap to estimate the variance of the sample average X. (No...

Read the case study International versus U.S. Standards Financial Accounting Theory and Analysis Case International versus U.S. Standards Under U.S. GAAP, property, plant, and equipment are reported...

Calculate pX,Y (0, 1) if pX,Y,Z (x, y, z) = For x, y, z =0, 1, 2, 3 and 0 x + y +z 3. 3-x-y-z 3! r!y!z!(3-x-y-z)!

. Corporations developed to encourage investors to contribute the capital needed to create large-scale manufacturing enterprises. But LLCs are often start-ups or other small businesses. Why do their...

Refer to the data of Exercise 22, and construct a control chart using the sin21 transformation as suggested in the text. Exercise 22 A sample of 200 ROM computer chips was selected on each of 30...

In some situations, the sizes of sampled specimens vary, and larger specimens are expected to have more defects than smaller ones. For example, sizes of fabric samples inspected for flaws might vary...

Construct a control chart for the data of Exercise 25 by using the transformation suggested in the text. Exercise 25 The accompanying observations are numbers of defects in 25 1-square-yard specimens...

Please help me answer this questions. Thank you in advance. WK Qu. 7-11 A firm has prepared the following binary... A firm has prepared the following binary integer program to evaluate a number of...

You make $5,400 annual deposits into a retirement account that pays 10.5 percent interest compounded monthly. Required: How large will your account balance be in 30 years? ( Enter rounded answer as...

Chap. 16 talks about some of the more common political risk characteristics. When a US company invests in China, which one of the political risk characteristics is most relevant and why? On the other...