DECISION THEORY EXERCISES 1. A revolutionary new process has been developed for the manufacture of golf balls. These golf balls are packaged in sets of three, and the manufacturer will sell a package of golf balls to a sporting goods wholesaler for $1.50. However, in order to become a distributor of these revolutionary new golf balls, the wholesaler agrees to one of two promotional actions. (a) Sell the package of golf balls for $2.50, agreeing to refund the entire purchase if one or more of the golf balls is found to be defective. (b) Sell the package of golf balls for $2.00, agreeing to refund $0.50 for each golf ball found to be defective. (1) Determine the loss table for this problem situation. (2) The wholesaler has determined the following set of information related to the number of defectives based upon testing 60 randomly selected test boxes. Quality of Test Ball 01: 0 defective States of Nature 02: 1 defective 03: 2 defectives 04:3 defectives Good Bad Total 11 4 15 10 7 3 6 7 12 16 14 15 Testing does not cost the wholesaler anything. A priori, wholesaler assumed that the probabilities associated with states of nature were as follows: P(01: 0 defective)=0.25 P(82: 1 defective) = 0.30 P(03: 2 defectives) = 0.20 P(84: 3 defectives) = 0.25 (A) What is the optimal Bayes' action before examining the test ball? (B) What are the optimal Bayes' actions given the two measures of quality of test balls? (C) What is the expected value of the optimal decision with the sample information? (D) What are the EVSI and EVPI for this problem?
DECISION THEORY EXERCISES 1. A revolutionary new process has been developed for the manufacture of golf balls. These golf balls are packaged in sets of three, and the manufacturer will sell a package of golf balls to a sporting goods wholesaler for $1.50. However, in order to become a distributor of these revolutionary new golf balls, the wholesaler agrees to one of two promotional actions. (a) Sell the package of golf balls for $2.50, agreeing to refund the entire purchase if one or more of the golf balls is found to be defective. (b) Sell the package of golf balls for $2.00, agreeing to refund $0.50 for each golf ball found to be defective. (1) Determine the loss table for this problem situation. (2) The wholesaler has determined the following set of information related to the number of defectives based upon testing 60 randomly selected test boxes. Quality of Test Ball 01: 0 defective States of Nature 02: 1 defective 03: 2 defectives 04:3 defectives Good Bad Total 11 4 15 10 7 3 6 7 12 16 14 15 Testing does not cost the wholesaler anything. A priori, wholesaler assumed that the probabilities associated with states of nature were as follows: P(01: 0 defective)=0.25 P(82: 1 defective) = 0.30 P(03: 2 defectives) = 0.20 P(84: 3 defectives) = 0.25 (A) What is the optimal Bayes' action before examining the test ball? (B) What are the optimal Bayes' actions given the two measures of quality of test balls? (C) What is the expected value of the optimal decision with the sample information? (D) What are the EVSI and EVPI for this problem?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:DECISION THEORY EXERCISES
1. A revolutionary new process has been developed for the manufacture of golf balls. These golf
balls are packaged in sets of three, and the manufacturer will sell a package of golf balls to a
sporting goods wholesaler for $1.50. However, in order to become a distributor of these
revolutionary new golf balls, the wholesaler agrees to one of two promotional actions.
(a) Sell the package of golf balls for $2.50, agreeing to refund the entire purchase if one or more
of the golf balls is found to be defective.
(b) Sell the package of golf balls for $2.00, agreeing to refund $0.50 for each golf ball found to
be defective.
(1) Determine the loss table for this problem situation.
(2) The wholesaler has determined the following set of information related to the number
of defectives based upon testing 60 randomly selected test boxes.
Quality of Test
Ball
01: 0 defective
States of Nature
02: 1 defective
03: 2 defectives 04:3 defectives
Good
Bad
Total
11
4
15
10
7
3
6
7
12
16
14
15
Testing does not cost the wholesaler anything. A priori, wholesaler assumed that the
probabilities associated with states of nature were as follows:
P(01: 0 defective)=0.25
P(82: 1 defective) = 0.30
P(03: 2 defectives) = 0.20
P(84: 3 defectives) = 0.25
(A) What is the optimal Bayes' action before examining the test ball?
(B) What are the optimal Bayes' actions given the two measures of quality of test balls?
(C) What is the expected value of the optimal decision with the sample information?
(D) What are the EVSI and EVPI for this problem?
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