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
▼ Random simple number
▼ Random Boolean number
▼ Bernoulli random boolean number
▼ Bernoulli series
Definition D208
Binomial random natural number
Formulation 0
Let $X_1, X_2, X_3, \, \dots \overset{d}{=} \text{Bernoulli}(\theta)$ 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}
Children
▶ D2854: Poisson random natural number
Results
▶ R5701
▶ R3199: Finite sum of uncorrelated Bernoulli random numbers is a binomial random number
▶ R3602: Gaussian approximation to binomial distribution
▶ R4948: Gaussian approximation to standard binomial distribution