# Today I Learned

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

## 19: Poisson Distribution

October 29, 2016

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

,

where 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 .

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