Definition:Bernoulli Trial

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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 $0 \le p \le 1$.[1]


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


Source of Name

This entry was named for Jacob Bernoulli.


Notes

  1. Some sources insist that $0 < p < 1$, but it can be useful in certain circumstances to include the condition when the outcome is certainty.