You are given the following payoff table (in units of thousands of Rands) for a decision Analysis
Problem. Show all formulas and calculations.
Alternatives State of Nature
S1 S2 S3
A1 25000 20000 14000
A2 23000 21000 19000
Prior Probability 0.6 0.3 0.1
(d) Using Bayes decision rule, do sensitivity analysis graphically with respect to the prior
probabilities of states S1 and S2 (without changing the prior probability of state S3) to
determine the crossover point where the decision shifts from one alternative to the other.
Then use algebra to calculate this crossover point. (6)
(e) Repeat part (d) for the prior probabilities of states S1 and S3. (6)
(f) Repeat part (d) for the prior probabilities of states S2 and S3. (6)
(g) If you feel that the true probabilities of the states of nature are within 10 percent of the
given prior probabilities, which alternative would you choose?