ThmDex – An index of mathematical definitions, results, and conjectures.

Two random real numbers identical in distribution have identical moments

Formulation 0

Let $X, Y \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that

(i)	\begin{equation} X \overset{d}{=} Y \end{equation}

Let $p \in [0, \infty)$ be an D4767: Unsigned real number such that

(i)	\begin{equation} \mathbb{E} X^p < \infty \end{equation}

Then \begin{equation} \mathbb{E} X^p = \mathbb{E} Y^p \end{equation}