Category:Definitions/Bernoulli Distribution

This category contains definitions related to Bernoulli Distribution.
Related results can be found in Category:Bernoulli Distribution.

Let $X$ be a discrete random variable on a probability space.

Then $X$ has the Bernoulli distribution with parameter $p$ if and only if:

$(1): \quad X$ has exactly two possible values, for example $\Img X = \set {a, b}$

$(2): \quad \map \Pr {X = a} = p$

$(3): \quad \map \Pr {X = b} = 1 - p$

where $0 \le p \le 1$.