The intuition of chance and probability develops at very early ages.1 However, a formal, precise definition of the probability is elusive. If the experiment can be repeated potentially infinitely many times, then the probability of an event can be defined through relative frequencies. For instance, if we rolled a die repeatedly, we could construct a frequency distribution table showing how many...

THE fundamental aim of education is the development of understanding: the mastery of concepts and procedures that permit the intelligent solution of problems in new and novel situations. In mathematics this goal is particularly challenging, for students are often adept at memorising the rules and formulas necessary to solve welldefined test and textbook problems, without ever coming to terms wi...

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. The present paper demonstrates that Kolmogorov’s (1933) formulation of probability theory admits a minimal generalization which includes improper priors and a general Bayes theorem. The resulting theory is closely related to the theory of conditional probability spaces formulated by Renyi...