The article “Uncertainty and Climate Change” 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.
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%.
(a) Under scenario A:
?= 0(0.65) + 5(0.2) + 15(0.1) + 25(0.05) = 3.75
(b) Under scenario B:
?= 0(0.65) + 5(0.24) + 15(0.1) + 20(0.01) = 2.90
(c) Under scenario C:
?= 0(0.65) + 2(0.24) + 5(0.1) + 10(0.01) = 1.08
(d) Let L denote the loss.
Under scenario A, P(L< 10) = P(L = 0) + P(L = 5) = 0.65 + 0.2 = 0.85.
Under scenario B, P(L< 10) = P(L = 0) + P(L = 5) = 0.65 + 0.24 = 0.89.
Under scenario C, P(L< 10) = P(L = 0) + P(L = 2) + P(L = 5) = 0.65 + 0.24 + 0.1 = 0.99.
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