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?

Question

Adolfo Fletcher

Mathematics

21 January, 03:23

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?

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Mckinley Horton · Answer 1

It defines 1280 possible outcomes

Step-by-step 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.