ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Binary cartesian set product ▼ Binary relation ▼ Map ▼ Simple map ▼ Simple function ▼ Measurable simple complex function ▼ Simple integral ▼ Unsigned basic integral ▼ Unsigned basic expectation ▼ Basic expectation ▼ Random real number moment
Definition D2013
Random real number central moment

Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
 (i) $p \in (0, \infty)$ is a D5407: Positive real number (ii) $$\mathbb{E} |X|^p < \infty$$
The central moment of $X$ with respect to $p$ and $\lambda \in \mathbb{R}$ is the D993: Real number $$\mathbb{E} \left[ (X - \lambda)^p \right]$$
Children
 ▶ Random real number kurtosis ▶ Random real number skewness
Results
 ▶ Basic real calculus expression for moments of centred gaussian random basic real number ▶ Expectation minimises second central moment for random real number ▶ Real calculus expression for moments of standard gaussian random real number