A university is applying classification methods in order to identify alumni who may be interested in donating money. The university has a database of 58,205 alumni profiles containing numerous variables. Of these 58,205 alumni, only 576 have donated in the past. The university has oversampled the data and trained a random forest of 100 classification trees. For a cutoff value of 0.5, the following confusion matrix summarizes the performance of the random forest on a validation set:

Predicted

Actual

Donation

No Donation

Donation

268

20

No Donation

5375

23439

The following table lists some information on individual observations from the validation set:

Observation ID

Actual Class

Probability of Donation

Predicted Class

A

Donation

0.8

Donation

B

No Donation

0.1

No Donation

C

No Donation

0.6

Donation

a. Explain how the probability of Donation was computed for the 3 observations. Why were observations A and C classified as Donation and observation B was classified as No Donation?

b. Compute the values of accuracy, true positive rate (TPR), false positive rate (FPR) and precision. Evaluate the performance of the classifier, particularly comment on the precision measure taking into account the natural occurrence of donors in the data set.