Definition:Expectation/Definition 2
Definition
The expectation of a random variable $X$ is the first moment about the origin of $X$.
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.
Also see
- Results about expectation can be found here.
Technical Note
The $\LaTeX$ code for \(\expect {X}\) is \expect {X}
.
When the argument is a single character, it is usual to omit the braces:
\expect X
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.