Question

A and B are discrete random variables. A can take on one of 20 possible values. B can take on one of 64 possible values. (In other words, the size of domain ( A ) is 20, and the size of domain ( B ) is 64.) How many possible outcomes does the joint distribution P ( A, B ) define probabilities for?

Answer 1

It defines 1280 possible outcomes

Explanation:

A can take on one of 20 possible values.Then, B can take on one of 64 possible values

The form to choose these pairs of outcomes are

(Possible values from A) x (Possible values from B) = 20 x 64 = 1280

Also the sum of these 1280 pairs of values must be equal to 1 because P(A,B) it is a joint distribution of probability.

We sum this 1280 pairs of values because A and B are discrete random variables.Otherwise we would use integrals.