The concept of independence in probability, called stochastic independence, was
introduced early in the history of the topic. If events form an independent class, then the …

Independence is a basic property of events and random variables in a probability model. Its
intuitive appeal stems from the easily envisioned property that the occurrence or non …

In Chapter 5, the concept of stochastic independence for classes of events is developed in
terms of a simple product rule. With due attention to some subtleties, this concept is …

In this article, we show that a finite collection of independent events cannot be exhaustive
except in the trivial case in which one of the events occurs with probability one. For an …

In Chapter 4, we introduced a mathematically simple characterization of stochastic
independence to model the lack of conditioning between two events. Independence is …

Knowing that an event has occurred sometimes forces us to reassess the probability of
another event; the new probability is the conditional probability. If the conditional probability …

Independence and Determination of Probabilities Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volumne 125, Number 12, December 1997, Pages …

Recall that two events A and B are independent if knowledge that B has occurred does not
change the probability that A will occur: that is, P (A| B)= P (A). This of course is algebraically …

For a set of random events, we introduce the notions of independence, partial
independence, dependence, and total dependence at a given level. For illustration …

3. Conditional Probability and Independence Page 1 3. Conditional Probability and
Independence Let A and B be two events defined on a probability space. Let fn(A) denote the …