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The article "Uncertainty and Climate Change" (G. Heal and

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 23SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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5
Problem 23SE

The article "Uncertainty and Climate Change" (G. Heal and B. Kriström, Environmental and Resource Economics, 2002:3-39) considers three scenarios, labeled A, B, and C, for the impact of global warming on income. For each scenario, a probability mass function for the loss of income is specified. These are presented in the following table.

 

Probability

Loss (%)

Scenario A

Scenario B

 

Scenario C

0

0.65

0.65

0.65

2

0

0

0.24

5

0.2

0.24

0.1

10

0

0

0.01

15

0.1

0.1

0

20

0

0.01

0

25

0.05

0

0

a. Compute the mean and standard deviation of the loss under scenario A.

b. Compute the mean and standard deviation of the loss under scenario B.

c. Compute the mean and standard deviation of the loss under scenario C.

d. Under each scenario, compute the probability that the loss is less than 10%.

Step-by-Step Solution:

Answer:

Step 1 of 5:  Consider three scenarios, labeled A, B, and C, for the impact of global warming on income. These are presented in the given table.

             

                   Probability

Loss (%)

Scenarios A

Scenarios B

Scenarios C

 0

0.65

 0.65

0.65

2

0

0

0.24

5

0.2

0.24

0.1

10

0

0

0.01

15

0.1

0.1

0

20

0

0.01

0

25

0.05

0

0

Step 2 of 5:  

a). To compute the mean and standard deviation of the loss under Scenarios A.

         

          The mean of Scenarios A:

       

 

            =  

            = 3.75.  

      The standard deviation of Scenarios A:

     

         =

         = 6.68.

Therefore, the mean and standard deviation of the loss under Scenarios A is 3.75 and 6.68.

Step 3 of 5:  

b). To compute the mean and standard deviation of the loss under Scenarios B.

         

             

          The mean of Scenarios B:

       

 

            =  

            = 2.9

     

   The standard deviation of Scenarios B:

     

         =

         = 4.91.

Therefore, the mean and standard deviation of the loss under Scenarios B is 2.9 and 4.91.

Step 4 of 5

Chapter 2, Problem 23SE is Solved
Step 5 of 5

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 23SE from 2 chapter was answered, more than 251 students have viewed the full step-by-step answer. This full solution covers the following key subjects: scenario, loss, compute, under, deviation. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 23SE from chapter: 2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “The article "Uncertainty and Climate Change" (G. Heal and B. Kriström, Environmental and Resource Economics, 2002:3-39) considers three scenarios, labeled A, B, and C, for the impact of global warming on income. For each scenario, a probability mass function for the loss of income is specified. These are presented in the following table. ProbabilityLoss (%)Scenario AScenario B Scenario C00.650.650.652000.2450.20.240.110000.01150.10.102000.010250.0500a. Compute the mean and standard deviation of the loss under scenario A.________________b. Compute the mean and standard deviation of the loss under scenario B.________________c. Compute the mean and standard deviation of the loss under scenario C.________________d. Under each scenario, compute the probability that the loss is less than 10%.” is broken down into a number of easy to follow steps, and 108 words.

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