38. A real estate development company, Omega, Inc., is considering the purchase of one of three "packages" put together by its director of marketing. Each package contains a different combination of land acreage by type of land, zoning, and geographic location. The value of the investment will depend on which of four population growth patterns occurs in the next few years. The payoff table is given below (in millions): Plan 1 2 3 4 Low 4,000,000 3,500,000 3,000,000 2,000,000 Demand Medium 4,250,000 4,750,000 4,250.000 3,500,000 High 4,500,000 5,000,000 7,500,000 12,500,000 a. Determine the Bayes decision, given the following probability density: P( 5₁ ) - 0.20, P( $₂ )-0.25, P( 3 )-0.45, and P(S)-0.10. b. Compute the expected value of perfect information. c. Suppose the marketing director spends P5,000,000 on market study and obtains some information, which we denote by 1. The conditional likelihood probabilities of I are as Ils, )-0.35, P( Ils, )-0.25. Determine follows: P( Ils, )-0.10, P( Ils₂ )-0.30, P the posterior Bayes decision. Was the P5,000,000 well spent?
38. A real estate development company, Omega, Inc., is considering the purchase of one of three "packages" put together by its director of marketing. Each package contains a different combination of land acreage by type of land, zoning, and geographic location. The value of the investment will depend on which of four population growth patterns occurs in the next few years. The payoff table is given below (in millions): Plan 1 2 3 4 Low 4,000,000 3,500,000 3,000,000 2,000,000 Demand Medium 4,250,000 4,750,000 4,250.000 3,500,000 High 4,500,000 5,000,000 7,500,000 12,500,000 a. Determine the Bayes decision, given the following probability density: P( 5₁ ) - 0.20, P( $₂ )-0.25, P( 3 )-0.45, and P(S)-0.10. b. Compute the expected value of perfect information. c. Suppose the marketing director spends P5,000,000 on market study and obtains some information, which we denote by 1. The conditional likelihood probabilities of I are as Ils, )-0.35, P( Ils, )-0.25. Determine follows: P( Ils, )-0.10, P( Ils₂ )-0.30, P the posterior Bayes decision. Was the P5,000,000 well spent?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:38. A real estate development company, Omega, Inc., is considering the purchase of one of three
"packages" put together by its director of marketing. Each package contains a different
combination of land acreage by type of land, zoning, and geographic location. The value of the
investment will depend on which of four population growth patterns occurs in the next few
years. The payoff table is given below (in millions):
Plan
Demand
Low
Medium
High
4,500,000
4,000,000
3,500,000
3,000,000
2,000,000
4,250,000
2
4,750,000
4,250.000
5,000,000
7,500,000
12,500,000
4
3,500,000
a. Determine the Bayes decision, given the following probability density: P( S: ) - 0.20, P(
$2 )-0.25, P( $ )-0.45, and P( S. )-0.10.
b. Compute the expected value of perfect information.
c. Suppose the marketing director spends P5,000,000 on market study and obtains some
information, which we denote by I. The conditional likelihood probabilities of I are as
follows: P( 1/s, -0.10, P( 11s, )-0.30, P( 11s, -0.35, PI 11s, )-0.25. Determine
the posterior Bayes decision. Was the P5, 000,000 well spent?
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