Probability Mass

probability-theory

Definition

Probability Mass

Let be the probability distribution of a random variable with state space . The probability mass carried by a value is the probability of its singleton:

For a discrete distribution, each possible value is a point in , and its mass is represented by a vertical lift. The height over is the probability of the singleton :

Contrast with Probability Density

Probability mass at is an actual probability and may be positive:

For a distribution described by a probability density, the density may be positive at while the singleton still has zero probability, . Probability is then carried by regions through integration rather than by individual points.

Example

Biased coin

Suppose records a coin toss with

The values and carry masses and . Their total mass is