Question

1. In Bayes rule: P (x|y) = P (y|x)P (x)/P (y), the P (y|x) is: (a) The prior probability. (b) The likelihood. (c) The posterior probability. (d) The conditional probability of y given x.

Answer 1

In Bayes' theorem, P(x|y) represents the posterior probability of event x given that event y has occurred.

The theorem is usually presented as follows: P(x|y) = P(y|x) * P(x) / P(y).

Here:

- P(x) is the prior probability. This is our initial degree of belief in x, before we have any evidence about y.

- P(y|x) is the likelihood. This is the probability of seeing the evidence y, given that event x is true.

- P(y) is the evidence. This is the total probability of seeing the evidence.

So, according to Bayes' rule, P(y|x) represents the likelihood of event y given that event x has occurred. Therefore, the correct answer is (b) The likelihood.