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Solved: Suppose that the proportion p of defective items

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish ISBN: 9780321500465 233

Solution for problem 4 Chapter 9.8

Probability and Statistics | 4th Edition

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Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Probability and Statistics | 4th Edition

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Problem 4

Suppose that the proportion p of defective items in a large manufactured lot is unknown, and it is desired to test the following simple hypotheses: H0: p = 0.3, H1: p = 0.4. Suppose that the prior probability that p = 0.3 is 1/4, and the prior probability that p = 0.4 is 3/4; also suppose that the loss from choosing an incorrect decision is 1 unit, and the loss from choosing a correct decision is 0. Suppose that a random sample of n items is selected from the lot. Show that the Bayes test procedure is to reject H0 if and only if the proportion of defective items in the sample is greater than log 7 6 + 1 n log 1 3 log 14 9

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Lecture 17 Nicole Rubenstein October 31, 2017 Multivariate distribution De▯nition 1.1. Let Y ;Y ;:::;Y be discrete random variables. The joint probability mass functions 1 2 n for Y1;Y2;:::;Ynare p(y1;y 2:::;y n = P(Y =1y ;Y1= 2 ;::2;Y = y n; n y12 S 1y 2 S ;:2:;y 2 n : n Theorem 1.1. If Y ;1 ;:2:;Y arn discrete random variable with joint probability mass function p(y1;y2;:::;y n, then 1. p(y1;y2;:::;yn) ▯ 0 for all 1 2 S1;y22 S ;2::;y 2nS : n P P P 2. ▯▯▯ p(y ;y ;:::;y ) = 1: y12S1 y22S2 yn2Sn 1 2 n Example 1.1. A local supermarket has three checkout counters. Two c

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Chapter 9.8, Problem 4 is Solved
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Textbook: Probability and Statistics
Edition: 4
Author: Morris H. DeGroot, Mark J. Schervish
ISBN: 9780321500465

Probability and Statistics was written by and is associated to the ISBN: 9780321500465. The full step-by-step solution to problem: 4 from chapter: 9.8 was answered by , our top Statistics solution expert on 01/12/18, 02:58PM. Since the solution to 4 from 9.8 chapter was answered, more than 239 students have viewed the full step-by-step answer. The answer to “Suppose that the proportion p of defective items in a large manufactured lot is unknown, and it is desired to test the following simple hypotheses: H0: p = 0.3, H1: p = 0.4. Suppose that the prior probability that p = 0.3 is 1/4, and the prior probability that p = 0.4 is 3/4; also suppose that the loss from choosing an incorrect decision is 1 unit, and the loss from choosing a correct decision is 0. Suppose that a random sample of n items is selected from the lot. Show that the Bayes test procedure is to reject H0 if and only if the proportion of defective items in the sample is greater than log 7 6 + 1 n log 1 3 log 14 9” is broken down into a number of easy to follow steps, and 127 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 102 chapters, and 1615 solutions. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4.

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Solved: Suppose that the proportion p of defective items