Question

1.In this task, we’ll assume that you are testing a classifier model that has a “true” classification error rate of 0.2 over the intended population of data instances; that is, for a given randomly selected instance of the population, the probability that the model predicts that instance’s class label incorrectly is 0.2. Note that you likely wouldn’t know the true error rate. Instead, you would need to estimate it based on a data sample.

(a) Suppose that you have access to three data instances selected independently at random from the population. What is the probability that the model will predict all of their class labels correctly? Explain.

(b) For a random sample of 10 instances selected independently, what is the probability that the model will make correct predictions on 8 of them, and incorrect prediction errors on the other two? Notice that it is not specified in advance which of the instances will receive correct predictions. Explain.

Answer 1

Let X be a Binomial random variable which denotes the number of instance for which the model predicts class label correctly

p = 1 - 0.2 = 0.8

(a) n = 3

The probability that the model will predict the class label correctly for all of the 3 instances = = 0.512

(b) Here n = 10

The required probability = P(X = 8)

= = 0.302