Independence of Events
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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 calculation of probabilities of Boolean combinations is highly simplified. In many applications, events of interest may be the result of processes that are operationally independent. That is, these processes are related in a such a manner that one process does not affect, nor is it affected by, the other. Thus the occurrence of an event associated with one of the processes does not affect the likelihood of the occurrence of an event associated with the other process. It would seem reasonable to suppose these events are independent in a probabilistic sense. The concept of stochastic independence can be represented mathematically by a simple product rule. In spite of the mathematical simplicity, logical consequences of this definition show that it captures much of the intuitive notion of independence and hence provides a useful model for applications. We introduce stochastic independence for a pair of events, examine some basic patterns, then extend the notion to arbitrary classes of events. We then identify a variety of patterns that indicate why the concept is both appropriate and useful.
KeywordsProduct Rule Null Event Equivalent Expression Intuitive Notion Boolean Combination
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