for independent random events is the basis of the binomial testing and the discrete probability distribution generated from the Bernoulli trial
is the binomial distribution.
We consider a sequence of Bernoulli trial
, and suppose that at each trial the bettor has the free choice of whether or not to bet.
The third chapter of Baxter's Handbook of Old Chinese (Berlin: Mouton de Gruyter, 1992) demonstrates, clearly but with no superfluous detail, how to use the probabilistic method called the Bernoulli trial
to study rhyming in a received Chinese corpus.
Specific topics described include injectivity of the Dubins-Freedman construction of random distributions, almost sure convergence of weighted sums of independent random variables, aperiodic order via dynamical systems, laws of iterated logarithm for weighted sums of iid random variables, and homeomorphic Bernoulli trial
measures and ergodic theory.
An event with dichotomous outcomes is typically modeled by a Bernoulli trial
. For a well-designed test, the chance of misgrading (p) is not high.
We begin by modeling the survival or failure of a nest over an interval t as a Bernoulli trial
with parameter [p.sup.t]: P(Y = y\p) = [([p.sup.t]).sup.y] [(1 - [p.sup.t]).sup.1 - y], where y is defined above and p is the daily survival probability of the nest.
As we mentioned in Section 2.2., a Standard Uniform U(0,1) variable can be used to model a binary process, that is, a Bernoulli trial
. Let p [member of] (0, 1) be fixed and let U [member of] U(0,1).