Ensemble

The ``true value'' of the mean could be defined as the mean that results when the coin is flipped n times, when n is conceived of as going to infinity. A more convenient definition of true value is that the experiment is imagined as having been done separately under identical conditions by an infinite number of people (an ``ensemble''). The ensemble may seem a strange construction; nonetheless, much literature in statistics and the natural sciences uses the ensemble idea. Let us say that the ensemble is defined by a probability as a function of time. Then the ensemble idea enables us to define a time-variable mean (the sum of the values found by the ensemble weighted by the probabilities) for, for example, coins that change with time.