Probability Mass Function (PMF) Calculator

When PMF is the right model

A probability mass function is used for a discrete random variable, where the outcomes are countable.

Each row pairs one possible outcome with its probability. Together the rows describe the full distribution.

Once the probabilities sum to 1, the mean and variance panels help you interpret the center and spread immediately.

Every probability should stay between 0 and 1.
Use repeated rows only if they represent distinct outcomes in your working notes.
Check $sum P(X=x)=1$ before treating the table as a full PMF.

Easily calculate the Moment Generating Function (MGF) for various probability distributions (PMF or PDF).

Calculate Cumulative Distribution Function (CDF) for discrete random variables online.

Effortlessly calculate the variance (Var[X]) of a discrete random variable online.