In probability and statistics, several terms are used to describe the various functions that are used to model probability distributions. These include:

**Probability density function (PDF):**

The PDF is a function that describes the probability of a **continuous** random variable **taking on a certain value**. It is a mathematical function that describes the probability that a random variable will fall within a certain range of values.

**Cumulative distribution function (CDF): **

The CDF is a function that describes the probability that a random variable (**continuous or discrete**) will **take on a value less than or equal to a certain value**. It is a mathematical function that describes the probability that a random variable will fall within a certain range of values, up to and including a specific value.

**Probability mass function (PMF): **

The PMF is a function that describes the probability of a **discrete** random variable **taking on a certain value**. It is a mathematical function that describes the probability that a random variable will take on a specific value rather than falling within a range of values.

## Summary:

In summary, PDFs are used to describe the probability of a continuous random variable taking on a certain value, CDFs are used to describe the probability that a random variable (continuous or discrete) will take on a value less than or equal to a certain value, and PMFs are used to describe the probability of a discrete random variable taking on a certain value.