Topics: Probability


A random variable is a measurable function ( a sample space) where, given any set :

…or also:

…where is a sigma-algebra.

In other words, a random variable is a mapping from the possible outcomes in the sample space to a measurable space (in this case ).

As such, in general, we can see a random variable as the mathematical formalisation of quantities or objects that depend on randomness.


There are two types of random variables:

For both of these, we can define a density function, which helps us specify the probability of the random variable being a certain value or being in a given interval.