Question

Consider the following joint probability mass function of two random variables x and y. a, b, and c are some fixed numbers:

Given the joint probability mass function, what is the fundamental property that it μst satisfy?
- A) ( sum_x sum_y P(x, y) = 0 )
- B) ( sum_x sum_y P(x, y) = 1 )
- C) ( sum_x P(x) = 0 )
- D) ( sum_x P(x) = 1 )

Answer 1

The joint probability mass function of two random variables must satisfy the property that the sum of all the probabilities for every possible combination of the variables equals 1.

Step-by-step explanation:

The fundamental property that the joint probability mass function (pmf) of two random variables x and y must satisfy is Option B) Σx Σy P(x, y) = 1. This property ensures that the total probability across all possible outcomes (the entire sample space) for x and y equals 1, which is a basic requirement of any probability distribution. In other words, when you add up all the probabilities for every possible combination of x and y, the sum must be equal to 1.