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.