Category:Binomial Distribution

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This category contains results about the binomial distribution.
Definitions specific to this category can be found in Definitions/Binomial Distribution.

Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Then $X$ has the binomial distribution with parameters $n$ and $p$ if and only if:

$\Img X = \set {0, 1, \ldots, n}$
$\map \Pr {X = k} = \dbinom n k p^k \paren {1 - p}^{n - k}$

where $0 \le p \le 1$.