Category:Bernoulli Distribution

From ProofWiki
Jump to navigation Jump to search

This category contains results about the 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 $0 \le p \le 1$.