Category:Bernoulli Trials
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This category contains results about Bernoulli Trials.
Definitions specific to this category can be found in Definitions/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.
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