**Probability mass function** (pmf) of a discontinuous random variable X is a function that satisfies the following requirements.

[Error: Macro 'mathequation' doesn't exist]
[Error: Macro 'mathequation' doesn't exist]

with [Error: Macro 'mathequation' doesn't exist]
being the probability of event [Error: Macro 'mathequation' doesn't exist]
.

In case of a continuous random variable X a probability density function is considered.