How to show inter arrival times are exponential in poisson distribution?
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The binomial distribution deals with the number of successes in a fixed number of independent trials, and
the geometric distribution deals with the time between successes in a series of independent trials.
Just so, the Poisson distribution deals with the number of occurrences in a fixed period of time, and the
exponential distribution deals with the time between occurrences of successive events as time flows by
continuously
If the mean interarrival time is 1/ (so is the mean arrival rate per unit time), then the variance will be 1/2 (and the standard deviation will be 1/ ). The graph below displays the graph of the exponential density function when = 1 . Generally, if X is exponentially distributed, then Pr(s < X t) = e-s - e-t (where e 2.71828) .
If the mean interarrival time is 1/ (so is the mean arrival rate per unit time), then the variance will be 1/2 (and the standard deviation will be 1/ ). The graph below displays the graph of the exponential density function when = 1 . Generally, if X is exponentially distributed, then Pr(s < X t) = e-s - e-t (where e 2.71828) .
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