Random variables and distributions

When assigning event probabilities, we could also try to cover the entire sample and assign one probability value to each of the possible outcomes for the sample domain.

This process does indeed have all the characteristics of a function, and thus we will have a random variable that will have a value for each one of the possible event outcomes. We will call this function a random function.

These variables can be of the following two types:

• Discrete: If the number of outcomes is finite, or countably infinite
• Continuous: If the outcome set belongs to a continuous interval

This probability function is also called probability distribution.