Definition:Expectation/Also known as

Expectation: Also known as

The expectation of a random variable $X$ is also called the expected value of $X$ or the mean value of $X$.

For a given random variable, the expectation 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.

$\mathsf{Pr} \infty \mathsf{fWiki}$ uses $\expect X$ for notational consistency.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): expectation (expected value)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): mean: 5.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): expectation (expected value)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): mean: 5.