Bernoulli trials

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Related to Bernoulli trial: binomial distribution, Geometric distribution

Bernoulli trials

[bər′nül·ē ‚trīlz]
(statistics)
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(16.) Such type of experiment, which has two possible outcomes, is called a Bernoulli trial. See Sidney Siegel; Non-parametric Statistics for the Behavioral Sciences; McGraw Hill Book Company.
Nest data were simulated by generating a uniform random variable, u (u = 1,...,25), representing the day a nest was found, then performing a Bernoulli trial with parameter ([[p.sup.[j.sub.1]].sub.1][[p.sup.[j.sub.2]].sub.2]) to determine whether the nest was still active on day u.
We present here one of the simplest methods, which is based on our earlier simulation of a Bernoulli trial. Let us revisit how a Bernoulli variable was generated.
Consider a series of n Bernoulli trials with probability of success p in every trial (q = 1 - p).
The step function will jump over and up with apparent randomness, but if the final statistic (after 162 games) ends up within the darkest gray (middle) region, then the runs statistic is within one standard deviation of the number of runs we would expect if the sequence was based on random Bernoulli trials. By graphing the path of the runs statistics, we are able to assess when and why a team's streaks were notable.
Therefore, to obtain a single estimate of the outage probability with random relay locations, we first approximate the first-hop error rates of the N relays by independent Bernoulli trials. Then, assuming that M out of N relays successfully decode the first-hop transmission from the source, we derive the second-hop outage probability for a given (deterministic) relay topology.
Testing this type of hypothesis involves estimating and comparing binomial parameters before and after the first occurrence of a success in a sequence of Bernoulli trials. By the nature of the process, the binomial parameter [p.sub.a] before the first occurrence of a success must be estimated under geometric sampling, that is, through the number of Bernoulli trials before the first success; on the other hand, the binomial parameter [p.sub.b] after the first success is estimated under binomial sampling, that is, through the number of successes in a fixed number of Bernoulli trials.
Thus, each key can be viewed as an infinite sequence of Bernoulli trials. This model is often called the Bernoulli model.