The article "Uncertainty and Climate Change" (G. Heal and B. Kriström, Environmental and Resource Economics, 2002:339) 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%.
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.