DeepAI # Continuous Random Variable

## What are Continuous Random Variables?

Continuous random variables are random variables can take values from an uncountable set, as opposed to discrete variables which must take values from a countable set.  Another way to put this is that a continuous random variable must be sampled from a distribution that yields an everywhere continuous cumulative distribution function. As a result, the probability that a random variable yields a specific number (in its range) is zero, and thus typically intervals of values are considered to obtain meaningful probability scores.

### How are Continuous Random Variables Used?

Continuous random variables are used to model stochastic processes that take values from a continuous range.  Some examples might be modeling temperature in some region or stock prices.  Although the latter (strictly speaking) does a have a countable range (prices are incremented by pennies), it is typically more mathematically convenient to use a continuous random variable.

In data science, a regression model tries to predict values for a continuous random variable (process) as opposed to a classification model which tries to predict values for a discreet random variable (process).