TABLE 19-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.
-Referring to Table 19-1, if the probability of S1 is 0.5, then the coefficient of variation for A1 is
A) 0.231.
B) 0.5.
C) 1.5.
D) 2.

Question

TABLE 19-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. 
-Referring to Table 19-1, if the probability of S1 is 0.5, then the coefficient of variation for A1 is
A) 0.231. 
B) 0.5. 
C) 1.5. 
D) 2.

Quizplus · Accepted Answer

To find the coefficient of variation for A1, we need to calculate the mean and standard deviation of its payoffs. The mean payoff for A1 is ((10+40+60)/3) = 36.67. The standard deviation can be found using the formula:
√(((10-36.67)² + (40-36.67)² + (60-36.67)²)/3) = 22.5
Therefore, the coefficient of variation is (22.5/36.67) = 0.61. 
However, since the probability of S1 is only 0.5, we need to adjust the coefficient of variation by multiplying it with the square root of the probability of S1 (i.e., √0.5). 
Thus, the adjusted coefficient of variation for A1 is (0.61 x √0.5) = 0.5. 
Therefore, the best choice is A1, as it has the highest expected payoff (36.67) and the lowest risk (coefficient of variation = 0.5).

TABLE 19-1 The Following Payoff Table Shows Profits Associated with a Set