Poisson Process Question
Assume that you perform and experiment where the outcomes occur according to a Poisson Process with rate 4 per minute, and that the experiment is complete once you observe 250 outcomes. Calculate the mean time and variance time of the experiment.
for the mean would think that it's just
but for the variance I'm not too sure but would think that it's
are these correct?
The interval between events has a exponential distribution with a mean of 1/4 min and a variance of (1/4)^2, so a SD of 1/4 min, also the intervals are independent RV's.
Originally Posted by lllll
Now you are looking at the sum of 250 such intervals so the mean is 250(1/4), and the SD is (1/4)*sqrt(250).
If I wanted to calculate the probability that the experiment finishes in less then 56.4 minutes? The would it follow: