Today I Learned

Some of the things I've learned every day since Oct 10, 2016

19: Poisson Distribution

The distribution of a discrete random variable X is considered a Poisson Distribution if, given an event x an given interval N (which can be thought of a number of chances x is given to occur), the probability of x occurring exactly k times on that size interval is given by

P(k \textrm{ occurrences}) = \frac{\lambda ^k e^{- \lambda}}{k!},

where \lambda is the known average of occurrences given an identical interval.

[Restrictions: events must occur independently, and no more than one instance of an event can happen at a single point in the interval.]

A couple nice properties of Poisson-distributed random variables are that the expected value and variance are both equal to \lambda.


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