## What is a Probability Density Function?

A Probability Density Function is a statistical expression used in probability theory as a way of representing the range of possible values of a continuous random variable. The area under the curve represents the interval of which a continuous random variable will fall, and the total area of the interval represents the probability that the variable will occur. The probability density function differs from a probability mass function that is used when calculating the probabilities of discrete random variables.

## How does a Probability Density Function work?

### Probability Density Functions and Machine Learning

A Probability Density Function is a tool used by machine learning algorithms and neural networks that are trained to calculate probabilities from continuous random variables. For example, a neural network that is looking at financial markets and attempting to guide investors may calculate the probability of the stock market rising 5-10%. To do so, it could use a Probability Density Function in order to calculate the total probability that the continuous random variable range will occur.