Definition:Bernoulli Distribution/Notation

Bernoulli Distribution: Notation

The Bernoulli distribution can be written:

$X \sim \Bernoulli p$

but as, from Bernoulli Process as Binomial Distribution, the Bernoulli distribution is the same as the binomial distribution where $n = 1$, the notation:

$X \sim \Binomial 1 p$

is often preferred, for notational economy.

Frequently $q$ is used for $1 - p$ in which case the probability mass function is given by:

$\map {p_X} x = \begin {cases} p & : x = a \\ q & : x = b \\ 0 & : x \notin \set {a, b} \\ \end {cases}$

where $p + q = 1$.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Bernoulli distribution