ThmDex – An index of mathematical definitions, results, and conjectures.
F13431
Formulation 1
Let $X_1, \, \ldots, \, X_N \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that
(i) $X_1, \, \ldots, \, X_N$ is an D2713: Independent random collection
Then \begin{equation} \mathfrak{F} \left( \sum_{n = 1}^N X_n \right) = \prod_{n = 1}^N \mathfrak{F} \left( X_n \right) \end{equation}