Question

Suppose the fire guard gives the following results after three months of use:                                                                                                                          

	State of the World
Response	Signal	Noise
Yes	38	24
Uncertain	10	10
No	6	15

1. How many times was the decision maker able to make the right decision for signal or noise in total if he is risk-averse?
2. What is the ratio of correct decisions to all decisions if the decision maker is risk seeking? Do you think that the guard is performing well? (if the ratio is greater than 0.75, that means the camera is performing well.)

Answer 1

When guard is risk averse, he rightly take ‘uncertain’ decision on Noise.

When guard is risk seeking, he rightly take ‘uncertain’ decision on Signal.

Confusion matrix:

Predicted Class Positive Negative Positive True Positive (TP) False Negative (FN) Type II Error Sensitivity ТР (TP + FN) Actual Class Negative False Positive (FP) Type I Error True Negative (TN) Specificity TN (TN + FP) Precision Negative Predictive Value TN (TN + FN) Accuracy TP + TN (TP + TN + FP + FN) ТР (TP + FP)

True Positive and True Negative are right decisions taken by the guard.

Excel Formulation:

1 A B с State of the world 2 Response Signal Noise 3 Yes 38 24 4 Uncertain 10 10 5 No 6 15 6 7 Risk Averse 8 True Positive =B3 9 True Negative =C5 10 Risk Aversion =C4 11 Total =SUM(B8:B10) 12 13 14 Right Decisions 15 True Positive =B3 16 True Negative =C5 Risk Seeking =B4 18 Total =SUM(B15:B17) 19 20 All Decisions =SUM(B3:05) 21 Ratio =B18/B20 17

1 2 3 5 A B с State of the world 2. Response Signal Noise Yes 38 24 4 Uncertain 10 10 5 No 6 15 6 7 Risk Averse 8 True Positive 38 9 True Negative 15 10 Risk Aversion 10 11 Total 63 12 13 14 Right Decisions 15 True Positive 38 16 True Negative 15 17 Risk Seeking 10 18 Total 63 19 20 All Decisions 103 21 Ratio 0.61165 22

a. 63 times right decisions for risk averse guard.

b. Ratio is 0.61165, lower than threshold of 0.75. that means guard is not performing well.

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