A decision maker is working on a problem that requires her to study the uncertainty surrounding the payoff of an investment. There are three possible levels of payoff — $1,000, $5,000, and $10,000. As a rough approximation, the decision maker believes that each possible payoff is equally likely. But she is not fully comfortable with the assessment that each probability is exactly 1/3, and so would like to conduct a sensitivity analysis. In fact, she believes that each probability could range from 0 to 1/2.
a. Show how a Monte Carlo simulation could facilitate a sensitivity analysis of the probabilities of the payoffs.
b. Suppose the decision maker is willing to say that each of the three probabilities could be chosen from a uniform distribution between0 and 1. Could you incorporate this information into your simulation? If so, how? If not, explain why not, or what additional information you would need.