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.
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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 variable. o X ~ Bernoulli (p) o The expectation of a Bernoulli distribution = the probability of success. (E[X]=p) o Variance [X] = p (1-p) o SD [X] = the square root of the variance Categorical nominal: o You can put the number of successes and failures into a bar plot. BINOMIAL DISTRIBUTION 0 1 When
Textbook: Probability and Statistical Inference
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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 298 students have viewed the full step-by-step answer.