Definition:Bernoulli Trial
From ProofWiki
Definition
A Bernoulli trial is an experiment whose sample space has two elements, which can be variously described, for example:
- Success and failure;
- True and False;
- $1$ and $0$;
- The classic heads and tails.
Formally, a Bernoulli trial is modelled by a probability space $\left({\Omega, \Sigma, \Pr}\right)$ such that:
- $\Omega = \left\{{a, b}\right\}$
- $\Sigma = \mathcal P \left({\Omega}\right)$
- $\Pr \left({a}\right) = p, \Pr \left({b}\right) = 1 - p$
where $0 \le p \le 1$.
That is, $\Pr$ obeys a Bernoulli distribution.
Source of Name
This entry was named for Jacob Bernoulli.
Notes
- ↑ Some sources insist that $0 < p < 1$, but it can be useful in certain circumstances to include the condition when the outcome is certainty.
