Difference between revisions of "Bernoulli experiment"
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The sum of ''n'' Bernoulli experiments with the same probability of success ''p'' follows a [[Binomial distribution]] ''B(n,p)''. | The sum of ''n'' Bernoulli experiments with the same probability of success ''p'' follows a [[Binomial distribution]] ''B(n,p)''. | ||
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Latest revision as of 03:08, July 13, 2016
A Bernoulli experiment (or Bernoulli trial) is the simplest non-trivial random experiment imaginable: it's an experiment of which the outcome is random and can be either of two possibilities: success and failure.
The standard example is tossing a coin.
Expectation and Variance
If the occurrence of a success is encoded as 1 and the occurrence of a failure with 0, then a probability of a success of p (and therefore, of a failure as q=1-p) leads to an expectation of
![{\displaystyle \mathbf {E} [X]=p\cdot 1+q\cdot 0=p}](https://wikimedia.org/api/rest_v1/media/math/render/svg/661189c0ee18c6a4505b5d710a11cee8d7957065)
The variance is .
![{\displaystyle Var(X)=\mathbf {E} [(X-\mathbf {E} [X])^{2}]=p(1-p)^{2}+q(0-p)^{2}=pq}](https://wikimedia.org/api/rest_v1/media/math/render/svg/963db881693ffae85365ea6d85f52b0ec755c782)
The sum of n Bernoulli experiments with the same probability of success p follows a Binomial distribution B(n,p).