Question 1. Decision Theory [7 Points]

There are two available diagnostic methods - D1 and D2 - to predict if a tissue sample is benign or malignant. Ninety percent of the samples processed are benign. The performance of the diagnostic methods are shown in the tables below:

Diagnostic Method: D1

Predicted: Benign

Predicted: Malignant

Actual: Benign

0.60

0.30

0.90

Actual: Malignant

0.04

0.06

0.10

Diagnostic Method: D2

Predicted: Benign

Predicted: Malignant

Actual: Benign

0.50

0.40

0.90

Actual: Malignant

0.02

0.08

0.10

There is no cost associated with a correct prediction.

a.The cost of predicting a malignant sample as benign is $4,000 and the cost of predicting a benign sample as malignant is $1,000. Which diagnostic method should a risk-neutral rational decision maker choose? Why? [3 Points]

b.Under what ranges of the cost of a predicting a malignant sample as benign is diagnostic method D2 the preferred choice? Assume that the cost predicting a benign sample as malignant remains $1,000 [4 Points].