# PDF, CDF and PMF – Probability Distribution Functions

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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.

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