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Suppose that we wish to test the hypotheses (9.8.1). Let

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

Solution for problem 5 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 5

Suppose that we wish to test the hypotheses (9.8.1). Let the loss function have the form of (9.8.2). a. Prove that the posterior probability of = 0 is 0f0(x)/[0f0(x) + 1f1(x)]. b. Prove that a test that minimizes r() also minimizes the posterior expected value of the loss given X = x for all x. c. Prove that the following test is one of the tests described in part (b): reject H0 if Pr(H0 true|x) w1/(w0 + w1

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Step 1 of 3

Chapter 2, Part One: Frequency Distributions, Histograms, and Related Topics 1. Frequency Distribution: paritions data into classes and assigns each class a frequency a. Frequency Tables: displays information in a frequency distribution, by listing each class along with its frequency b. Constructing a Frequency Table i. Decide on a number of classes between 5 and 15 ii. Calculate the class width 1. (Highest Value­Lowest Value) / (# of Classes) a. (# of Classes)  What was chosen in step one b. then,

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Chapter 9.8, Problem 5 is Solved
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Textbook: Probability and Statistics
Edition: 4
Author: Morris H. DeGroot, Mark J. Schervish
ISBN: 9780321500465

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Suppose that we wish to test the hypotheses (9.8.1). Let