Instruction 17-3
The following payoff matrix is given in dollars.
Suppose the probability of Event 1 is 0.5 and Event 2 is 0.5.
-Referring to Instruction 17-3,the coefficient of variation for Action A is
A)12.8%.
B)33.3%.
C)333.3%.
D)133.33%.

Question

Quizplus · Accepted Answer

To calculate the coefficient of variation, we need to first calculate the expected value and standard deviation of the payoffs for each action.
For Action A: 
Expected value = (500*0.5) + (1000*0.5) = 750 
Standard deviation = sqrt(((500-750)^2*0.5) + ((1000-750)^2*0.5)) = 250

Coefficient of variation = (standard deviation / expected value) * 100% = (250/750) * 100% = 33.3%

For Action B: 
Expected value = (1000*0.5) + (0*0.5) = 500 
Standard deviation = sqrt(((1000-500)^2*0.5) + ((0-500)^2*0.5)) = 500

Coefficient of variation = (standard deviation / expected value) * 100% = (500/500) * 100% = 100%

Therefore, Action A has a lower coefficient of variation, indicating less risk than Action B. Thus, the best choice is to choose Action A.

Instruction 17-3 The Following Payoff Matrix Is Given in Dollars