DeepAI # Probability Density Function

## 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.

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## How does a Probability Density Function work?

The Probability Density Function works by conceptualizing the probabilities of a continuous random event occurring by defining a range, or interval. For example, if one wanted to calculate the probability that a specific temperature, say 70 degrees, will be reached, they may turn to a probability mass function, as the variable is defined in discrete terms. However, if one wanted to calculate the probability that a temperature between 70-75 degrees will be reached, they may use a probability density function, as the variable is defined as a range with infinite discrete values. Since the Probability Density Function defines probabilities with intervals, the probability of a single discrete value is defined as zero, since it does not have a range.

### 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.