Discrete Random Variable PMF Calculator

Easily calculate and visualize the Probability Mass Function (PMF) for discrete random variables.

Input Values and Probabilities

Enter the values of your discrete random variable and their corresponding probabilities, separated by commas.

Random Variable Values (x)

Comma-separated values.

Probabilities P(X=x)

Comma-separated probabilities (0 to 1).

What is a Probability Mass Function (PMF)?

In probability theory, a Probability Mass Function (PMF) is used to describe the probability distribution of a discrete random variable. The PMF gives the probability that a discrete random variable is exactly equal to some value. In other words, for each possible value that the random variable can take, the PMF tells us the probability of observing that value. For a valid PMF, the sum of probabilities for all possible values must equal 1, and each probability must be between 0 and 1, inclusive. This calculator helps you generate the PMF table given a set of values and their probabilities, and also validates if the provided probabilities form a valid PMF.

Discrete Random Variable: A variable whose value can only take on a countable number of values.
PMF Purpose: To provide probabilities for each outcome of a discrete random variable.
Sum of Probabilities: Must always equal 1 for a valid PMF.