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A generalization of ‘expectation equals reciprocal of intensity' to non-stationary exponential distributions

Published online by Cambridge University Press:  14 July 2016

Eugene A. Feinberg*
Affiliation:
SUNY at Stony Brook
*
Postal address: Harriman School for Management and Policy, SUNY at Stony Brook, Stony Brook, NY 11794–3775, USA.

Abstract

An observer watches one of a set of Poisson streams. He may switch from one stream to another instantaneously. If an arrival occurs in a stream while the observer is watching another stream, he does not see the arrival. The experiment terminates when the observer sees an arrival. We derive a formula which states essentially that the expected total time that the observer watches a stream is equal to the probability that he sees the arrival in this stream divided by the intensity of the stream. This formula is valid independently of the observation policy. We also discuss applications of this formula.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1994 

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References

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