Question

Let H be a class of binary classifiers over a set Z. Let D be an unknown distribution over X, and let g be a target hypothesis.

Answer 1

To show that events G and H are independent, we compare the probability of their intersection to the product of their individual probabilities. If they are equal, then G and H are independent.

Step-by-step explanation:

In order to show that events G and H are independent, we need to show that the probability of their intersection, P(GH), is equal to the product of their individual probabilities, P(G) and P(H). In this scenario, we are given that P(G) = 0.6, P(H) = 0.5, and P(GH) = 0.3. To determine independence, we need to compare P(GH) and P(G)P(H). If they are equal, then G and H are independent. In this case, we have:

P(G)P(H) = (0.6)(0.5) = 0.3

Since P(GH) = 0.3, which is equal to P(G)P(H), we can conclude that events G and H are independent.