Category:Definitions/Binomial Experiments

This category contains definitions related to Binomial Experiments.
Related results can be found in Category:Binomial Experiments.

A binomial experiment is a sequence (either finite or infinite) of Bernoulli trials, each of which has the same parameter $p$.

That is, a binomial experiment (with parameter $p$) is a sequence $\sequence {X_i}$ (either finite or infinite) such that:

$(1): \quad$ the value of each $X_i$ is one of two values (for example: $a$ or $b$).

$(2): \quad$ the probability that $X_i = a$ is the same for all $i$ (for example: $p$).

$(3): \quad$ the outcomes of all the Bernoulli trials are independent.

That is, it is a sequence of experiments, all of which can be modelled by the same Bernoulli distribution.