Binomial distribution¶
Story¶
We perform \(N\) Bernoulli trials, each with probability \(\theta\) of success. The number of successes, \(n\), is Binomially distributed.
Example¶
Distribution of plasmids between daughter cells in cell division. Each of the \(N\) plasmids as a chance \(\theta\) of being in daughter cell 1 (“success”). The number of plasmids, \(n\), in daughter cell 1 is Binomially distributed.
Parameters¶
There are two parameters: the probability \(\theta\) of success for each Bernoulli trial, and the number of trials, \(N\).
Support¶
The Binomial distribution is supported on the set of nonnegative integers less than or equal to \(N\).
Probability mass function¶
\[\begin{split}\begin{align}
f(n;N,\theta) = \begin{pmatrix}
N \\
n
\end{pmatrix}
\theta^n (1\theta)^{Nn}.
\end{align}\end{split}\]
Usage¶
Package 
Syntax 

NumPy 

SciPy 

Stan 
