Category:Definitions/Bernoulli Trials

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

A Bernoulli trial is an experiment whose sample space has two elements, which can be variously described, for example, as:

Success and failure

True and False

$1$ and $0$

the classic heads and tails.

Formally, a Bernoulli trial is modelled by a probability space $\struct {\Omega, \Sigma, \Pr}$ such that:

$\Omega = \set {a, b}$

$\Sigma = \powerset \Omega$

$\map \Pr a = p, \map \Pr b = 1 - p$

where:

$\powerset \Omega$ denotes the power set of $\Omega$

$0 \le p \le 1$

That is, $\Pr$ obeys a Bernoulli distribution.

Source of Name

This entry was named for Jacob Bernoulli.