# Simplifying our notation about expectations

# Simplifying our notation about expectations¶

We saw that for discrete random variables we need to write:

\[
\mathbf{E}[X] = \sum_x xp(x),
\]

while for a continuous random variable we need to write:

\[
\mathbf{E}[X] = \int_{-\infty}^{+\infty} xp(x).
\]

Let’s make the following convention. We are going to write:

\[
\mathbf{E}[X] = \int xp(x),
\]

no matter what the nature of \(X\) is is. If it is discrete, we will sum over its values. If it is continuous, we will integrate over its values. This is the notation most commonly used in practice.