Probabilistic description of radioactivity based on the good-as-new postulate

Abstract

The good-as-new postulate applied to radioactivity says: The conditional probability that a radioactive atom will ’’live’’ past time s+t, given that it has lived past time s, is equal to the unconditional probability that it would have lived past time t, starting from time zero. This postulate leads directly to the conclusion that the decay time of a radioactive atom is an exponentially distributed random variable. Add the postulate that the decay times of individual atoms in an aggregrate of identical radioactive atoms are independent, and a complete description of the random behavior of an aggregrate can be constructed. This approach stresses from the outset the randomness inherent in the radioactive decay process and is offered as a complement to the deterministic approach that treats fluctuations about mean values. All results are exact within the context of the model and are applicable to aggregrates of any size—no assumptions about large numbers are required.

Random sampling of an alternating current source: A tool for teaching probabilistic observations

“…The pedagogy of probability for physics students has received attention, with many proposals of statistics-oriented experiments 2,3,4,5 and theoretical expositions 6,7,8,9 , providing interesting insights. A more physical example of radioactive decay, a natural random (quantum) process has also been used to teach and demonstrate probabilistic ideas 10,11,12,13 . However, a typical physics laboratory requires more experiments involving probability distributions and their manipulation.…”