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A proportion is the fraction of some total that is of a particular kind, either (i) as a count of one type of thing out of a total count, or (ii) as a component of a continuous variable.
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Bernoulli / binomial trials for a process with variable probability of success
One of the conditions for a Bernoulli trial (and by extension binomial proportion confidence intervals) is that the probability of success is the same every time the experiment is conducted. … In the case of a process that has some degree of unavoidable variability in it (e.g. p = 0.8 $\pm$ 0.1), is this still a Bernoulli trial (and can binomial proportion confidence intervals still be calculated …