Richard von Mises Quotes

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.

Remember that algebra, with all its deep and intricate problems, is nothing but a development of the four fundamental operations of arithmetic. Everyone who understands the meaning of addition, subtraction, multiplication, and division holds the key to all algebraic problems.

The main interest of physical statistics lies in fact not so much in the distribution of the phenomena in space, but rather in their succession in time.

In games of chance, in the problems of insurance, and in the molecular processes we find events repeating themselves again and again. They are mass phenomena or repetitive events.

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.

I am prepared to concede without further argument that all the theoretical constructions, including geometry, which are used in the various branches of physics are only imperfect instruments to enable the world of empirical fact to be reconstructed in our minds.

Because certain elements of geometry have for a long time been included in the general course of education, every educated man is able to distinguish between the practical task of the land surveyor and the theoretical investigation of the geometer. The corresponding distinction between the theory of probability and statistics has yet to be recognized.

Insurance companies nowadays apply the principle of so-called 'selection by insurance'; this means that they take into consideration the fact that persons who enter early into insurance contracts are on the average of a different type and have a different distribution of death ages from persons from persons admitted to the insurance at a more advanced age.

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 theory of probability can never lead to a definite statement concerning a single event.

Apart from this older generation, there is scarcely a modern mathematician who still adheres without reservation to the classical theory of probability. The majority have more or less accepted the frequency definition.

If the concept of probability and the formulae of the theory of probability are used without a clear understanding of the collectives involved, one may arrive at entirely misleading results.

I do not want to defend the occult sciences; I am, however, convinced that further unbiased investigation of these phenomena by collection and evaluation of old and new evidence, in the usual scientific manner, will lead us sooner or later to the discovery of new and important relations of which we have as yet no knowledge, but which are natural phenomena in the usual sense.

No contradiction exists, if the events are correctly interpreted.

The whole financial basis of insurance would be questionable if it were possible to change the relative frequency of the occurrence of the insurance cases (deaths, etc.) by excluding, for example, every tenth one of the insured persons, or by some selection principal.