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# Solution: Let X1,X2, . . . ,Xn be a random sample from a ISBN: 9780321923271 41

## Solution for problem 5E Chapter 6.9

Probability and Statistical Inference | 9th Edition

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Problem 5E

Let X1,X2, . . . ,Xn be a random sample from a gamma distribution with α = 1, θ. Let h(θ) ∝ 1/θ, 0 <θ < ∞, be an improper noninformative prior.

(a) Find the posterior pdf of θ.

(b) Change variables by letting z = 1/θ, and show that the posterior distribution of Z is .

(c) Use 2yz to obtain a (1 − α) probability interval for z and, of course, for θ.

Step-by-Step Solution:
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STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION  In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0.  Probability of success is represented by a p.  For a Bernoulli random...

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##### ISBN: 9780321923271

This full solution covers the following key subjects: distribution, posterior, let, obtain, ind. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The full step-by-step solution to problem: 5E from chapter: 6.9 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “Let X1,X2, . . . ,Xn be a random sample from a gamma distribution with ? = 1, ?. Let h(?) ? 1/?, 0 <? < ?, be an improper noninformative prior.(a) Find the posterior pdf of ?.(b) Change variables by letting z = 1/?, and show that the posterior distribution of Z is .(c) Use 2yz to obtain a (1 ? ?) probability interval for z and, of course, for ?.” is broken down into a number of easy to follow steps, and 72 words. Since the solution to 5E from 6.9 chapter was answered, more than 244 students have viewed the full step-by-step answer.

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