A random variable is a variable that has a value, but there are uncertainty with respect to what that value is.

**discrete**: finite number of values**continuous**: infinitely many possible values

## probability mass function

A discrete random variable is encoded as a probability mass function

## probability density function

A continuous random variable is represented as a probability density function.

## summary statistics

- probability mass function is a description for the random variable: and random variables are usually communicated via probability mass functions
- expected value

## adding random variables

“what’s the probability of \(X + Y = n\)”?

\begin{equation} \sum_{i=0}^{n} P(X=i, Y=n-i) \end{equation}

for every single outcome, we want to create every possible operation which causes the two variables to sum to \(n\).