Do all random variables dealing with number of random, independent events in a continuous interval follow a Poisson distribution?
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No. $ $ $ $ $ $ – Did Sep 08 '14 at 14:57
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The Poisson distribution has the property that the chance of an event in a time $\delta t$ is $\lambda\cdot\delta t$. – almagest Sep 08 '14 at 15:01
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That is a somewhat vague way of putting it, which could probably be construed in ways that would amount to a false statement. The things that are independent must be counts in non-intersecting subintervals. ${}\qquad{}$ – Michael Hardy Sep 08 '14 at 15:30
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So where exactly can poisson distributions be used? – Kishore Sep 10 '14 at 00:56