Mass phenomena to which the theory of probability does not apply are, of course, of common occurrence. - Richard von Mises

Equally possible cases do not always exist, e.g, they are not present in the game with a biased die, or in life insurance. Strictly speaking, the propositions of the classical theory are therefore no applicable to these cases.

The mean and variance are unambiguously determined by the distribution, but a distribution is, of course, not determined by its mean and variance: A number of different distributions have the same mean and the same variance.

It is useful to have a short expression for denoting the whole of the probabilities attached to the different attributes in a collective. We shall use for this purpose the word distribution.