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week6 - Poisson Processes Model for times of...

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week 6 1 Poisson Processes Model for times of occurrences (“arrivals”) of rare phenomena where λ – average number of arrivals per time period. X – number of arrivals in a time period. In t time periods, average number of arrivals is λ t . How long do I have to wait until the first arrival? Let Y = waiting time for the first arrival (a continuous r.v.) then we have Therefore, which is the exponential cdf. The waiting time for the first occurrence of an event when the number of events follows a Poisson distribution is exponentially distributed.
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