Expectation

$E[f(x)]$ — the expected value of f under x's distribution.

Expectation(f, Distributed(x, dist))exact for f constant, linear or quadratic in x; otherwise stays unevaluated.

Typed signatures

Type	Package	Applies
`(any, expression<Distributed>) -> real`	`statistics`	always

Domain: Statistics

Details

Closed forms: $E[c] = c$ ; $E[x] = Mean(dist)$ ; $E[x^2] = Variance(dist) + Mean(dist)^2$ ; extended over Add and Multiply-by-constant by linearity — $E[2x+1] = 2\,E[x]+1$ , and so on, recursively.
Never approximated on its own — apply N to the result for a numeric value.
Anything past a linear/quadratic polynomial in x (e.g. $E[\sin x]$ ) has no closed form here and stays unevaluated, rather than falling back to numeric integration.