# Definition:Expectation/Also known as

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## Expectation: Also known as

The **expectation** of a random variable $X$ is also called the **expected value of $X$** or the **mean of $X$**, and (for a given random variable) is often denoted $\mu$.

The terminology is appropriate, as it can be seen that an **expectation** is an example of a normalized weighted mean.

This follows from the fact that a probability mass function is a normalized weight function.

Various forms of $E$ can be seen to denote **expectation**:

- $\map E X$
- $\map {\mathrm E} X$
- $E \sqbrk X$
- $\mathop {\mathbb E} \sqbrk X$

and so on.