Category:Definitions/Binomial Distribution

This category contains definitions related to Binomial Distribution.
Related results can be found in Category: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 $0 \le p \le 1$.