Probability function (for a discrete random variable)

A mathematical function that provides a model for the probability of each value of a discrete random variable occurring.

For a discrete random variable that has a finite number of possible values, the function is sometimes displayed as a table, listing the values of the random variable and their corresponding probabilities.

A probability function has two important properties:

• For each value of the random variable, the values of a probability function are never negative or greater than 1.
• The sum of the values of a probability function, taken over all of the values of the random variable, is 1.

Example 1

Let X be a random variable with a binomial distribution with n = 6 and π = 0.4. The probability function for a random variable X is:

Probability of x successes in 6 trials, P(X = x) = 

for x = 0, 1, 2, 3, 4, 5, 6

where:

is the number of combinations of n objects taken x at a time.

A graph of this probability function is shown below.

Example 2

Imagine a probability activity in which a fair die is rolled and the number facing upwards is recorded. Let the random variable X represent the result of any roll.

The probability function for random variable X can be written as:

Alternative: probability model

See: model

Curriculum achievement objectives reference

Probability: Level 8

The quality of the images on this page may vary depending on the device you are using.