ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Simple map
Simple function
Measurable simple complex function
Random simple number
Random Boolean number
Bernoulli random boolean number
Bernoulli series
Definition D208
Binomial random natural number
Formulation 0
Let $X_1, X_2, X_3, \dots \in \text{Bernoulli}(\theta)$ each be a D207: Bernoulli random boolean number such that
(i) $X_1, X_2, X_3, \dots$ is an D2713: Independent random collection
A D5216: Random natural number $B \in \text{Random}(\mathbb{N})$ is a binomial random natural number with parameters $N \in \mathbb{N}$ and $\theta$ if and only if \begin{equation} B \overset{d}{=} \sum_{n = 1}^N X_n \end{equation}
Gaussian approximation to binomial distribution
Gaussian approximation to standard binomial distribution