Overview
A random variable is a real valued function defined on a set of possible outcomes called a probability space.
Topics
Comparison of Density and Cumulative
The following plots out the probability density and cumulative probability function for the normal distribution.
Formal Definition
The exact technical requirements for a function to be considered a random variable is that the function is measurable. This requirement ensures that a probability can be assigned to events which represent specified values of the random variable. For example, it can be asked what the probability of a given value or range of values of the random varialbe is.