Data Mining Question

Consider a test data of 1000 samples with two classes: + class (100 samples) and class (900 samples). We have two random classifiers C1 and C2. Classifier C1 classifies test data to + class randomly with a probability p and classifier C2 classifies test data to + class randomly with a probability 2p.

a) What is the expected TPR and FPR for C1 and C2?

b) Is C2 a better classifier than C1? Hint: The random guess line in an ROC curve corresponds to TPR = FPR.

c) Expected precision for both C1 and C2 is 1/10. Expected recall for C2 is twice than that of C1 (2p and p respectively). If we use precision and recall as the evaluation metrics, C2 appears to be a better classifier than C1. Which evaluation metric pair between {TPR and FPR} and {precision and recall} do you think is correctly indicating the relative performance of C2 and C1?