On the construction of independence counterexamples
Date
2010-04-29T19:44:19Z
Authors
Johnson, Bruce R.
Tilly, Benjamin J.
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Abstract
A simple method of modifying probability to create independence counterexamples is given. This method can be used to construct counterexamples for finite collections of events and for infinite sequences of events. It is shown how to construct examples of countable collections of events where all equations in the (countable) family of "product rules" that define independence of the events that are satisfied except for one, or, more generally, except for an arbitrarily specified subfamily.
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Keywords
counterexamples, dependence, independence, random events, teaching of probability, teaching of mathematical statistics