## What is the difference between continuous and discrete random variables?

## Answer

Discrete and continuous random variables have different ranges. The range of a discrete distribution is countable, while the range of a continuous variable is not. However, countable is not the same as finite. For example, in an experiment where the random variable is defined as the number of coin flips until the first head, the range is infinite but still countable.

A less mathematical way to describe the difference is to say that discrete random variables are used for counting, and continuous random variables are used for measuring. Discrete random variables are used for experiments such as flipping a coin or rolling a six-sided die, while continuous random variables can be used to describe variables like weight or income.

Mathematically, it’s important to remember that summation is used to find a range of probabilities for discrete random variables and integration is used for continuous random variables.