Probability distribution of

Tan Tian-rong

It is expounded that a statistical distribution is a realistic distribution, while a probability distribution is its idea image; a statistical distribution is objective distribution, while a probability distribution depends on observers. In quantum mechanics, the confusion between statistical distributions and probability distributions creates two mistakes: misreading a probability distribution as a realistic distribution and misreading a subjective uncertainty as an objective uncertainty. Schrodinger' s cat is an imagery that opens out these two mistakes.

Philippe Réfrégier

Tânia Tomé, Mário J. de Oliveira

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko

Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability distribution is considered.

Roberto Piazza

Lawrence Sklar

The probability of an outcome was taken to be something closely related to the frequency with which that outcome could be expected to occur in a large number of identical repeated trials of some specified kind. A fundamental theorem of probability theory, Bayes' Theorem, relates the probability of a hypothesis on the basis of evidence to the conditional probability of the evidence, given the truth of the hypothesis and the initial probability that the hypothesis is true. "Nonpathological" means, essentially, that the initial probability distribution will give probability zero to any region of microconditions that have zero probability in the familiar, standard measure. Any non-pathological initial probability distribution for a mixing system will, as time goes into past infinity, also evolve into a probability distribution that is coarsely like the equilibrium distribution. The probability distribution is rationalized by showing that it is the uniquely stationary one that gives probability zero to regions given probability zero in that very natural measure.