THROUGH LONG PERIODS OF TIME.
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while the probabilities of subsequent events may often be determined from the probabilities of prior events, it is rarely the case that probabilities of prior events can be determined from those of subsequent events, for we are rarely justified in excluding the consideration of the antecedent probability of the prior events.
It is worthy of notice that to take a system at random from an ensemble at a date chosen at random from several given dates, , , etc., is practically the same thing as to take a system at random from the ensemble composed of all the systems of the given ensemble in their phases at the time , together with the same systems in their phases at the time , etc. By Theorem VIII of Chapter XI this will give an ensemble in which the average index of probability will be less than in the given ensemble, except in the case when the distribution in the given ensemble is the same at the times , , etc. Consequently, any indefiniteness in the time in which we take a system at random from an ensemble has the practical effect of diminishing the average index of the ensemble from which the system may be supposed to be drawn, except when the given ensemble is in statistical equilibrium.
