## What is a Random Variable?

The term "Random Variable" is used extremely often within the realm of probability and statistics, but what does it mean? Well, a random variable is defined as a variable whose possible values are outcomes of a random phenomenon. In specific terms, it is a function that maps the outcomes of an unpredictable process in numerical terms, often represented as a real number. So, a random variable may represent the outcome of an experiment that has yet to be performed, or a value that is currently uncertain. However, there are a couple of properties that are required of random variables.

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Random variables have a domain defined by the set of all possible outcomes of an event. Additionally, they have a probability distribution. This distribution can be either continuous, measuring numerical values in an interval, or discrete, as specified by a list of countable values. Within probability theory, random variables are used as functions defined by a sample space whose outcomes are numerical values.

## Applications of Random Variables

### Discrete - Coin Toss

### Continuous - Height

Any random variable that is defined through measuring, rather than counting, is continuous. In this case, imagine wanting to study the effects of caffeine intake on height. One's height would be the continuous random variable as it is unknown before the completion of the experiment, and its value is taken from measuring within a range.

### Random Variables in Machine Learning

Random variables are an invaluable tool within applications of machine learning. As a neural network makes decisions using machine learning, it creates functions for understanding possible outcomes. These possible outcomes are often defined by random variables. Â