Probability theory and stochastic processes Concept
Bernoulli trial
Builds on Random experiment
Summary
A Bernoulli trial is a random experiment with exactly two possible outcomes, called success and failure. The probability of success is the same each time the trial is repeated, and the failure has probability . A sequence of Bernoulli trials usually means independent repetitions of one trial. The number of successes in such trials has the binomial distribution.
Remarks
The outcome of one trial, coded as for success and for failure, has the Bernoulli distribution. The trials are named after Jacob Bernoulli, who studied them in his book Ars Conjectandi of 1713. Examples are a coin toss, with heads as success, and a roll of a die, with a six as success and .
Reading path
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- no evidence level
- Random experiment concept
- Bernoulli trial concept
Where this leads
15 pages build on this one.
- Bernoulli process
- De Moivre–Laplace theorem
- Mean of the geometric distribution
- Bernoulli distribution
- Coupon collector's problem
- Expectation with respect to the binomial distribution
- Binomial distribution
- Geometric distribution
- Poisson limit theorem
- Negative binomial distribution
- Memorylessness
- Wilcoxon signed-rank test
- Minimum-variance unbiased estimator
- Sign test
- Binomial proportion confidence interval
Further reading
- Web https://en.wikipedia.org/wiki/Bernoulli_trial, lead section
About this page
| Tag | 0PHC9FE2V5 |
|---|---|
| URI | m2://0PHC9FE2V5 |
| Aliases | binomial-trial |
| Kind | concept |
| Writing | W0 stub |
| MSC | 60A05 |
| Specializes | Random experiment |
| Uses | Random experiment |
| Same as |
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