Poisson Distribution

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Last updated 3:48 PM on 10/6/26
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11 Terms

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poisson distribution

a discrete probability distribution that applies to occurrences of some event over a specified interval. the interval can be time, space, distance, area, volume, or some similar unit. the random variable, X, is the number of “successes”

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what are “successes” in a poisson distribution

the number of occurrences of the event in the specified interval

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what makes the poisson distribution different from the binomial distribution

the binomial has a fixed number of trials and therefore, a limit to the number of times the outcome we want can happen. the poisson has a fixed interval of time or space in which the number of “successes” can be recorded, but there is no limit to the number of “successes”

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example of poisson vs binomial

  • binomial: n=4, then at most x=4

  • poisson: fixed interval is 1 day and there is no limit to the number of times the outcome of the interval can happen in that day


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assumptions of a poisson distribution

1) events must occur one at a time, and occurrences of the events are independent

2) theoretically, an infinite number of occurrences of the event must be possible in the interval

3) the probability of a single occurrence of the event in a given interval is proportional to the length of the interval

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<p>what is this formula</p>

what is this formula

poisson probability formula

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what is mu in the poisson probability formula

the average number of occurrences of the random event in the specified interval

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what is e in the poisson probability formula

~ 2.71828

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if the poisson distribution question says “at least” why does that change things

because we have no idea what the upper bound would be

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what to do if the poisson distribution question says “at least,” with at least 3 being the example

P(x greater than or equal to 3) + P(x less than or equal to 3) = 1

  • this is complementary so it can also be:

P(x greater than or equal to 3) = 1-P(x less than 3)

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when there is “at least” in the poisson distribution question, what does the complementary equation used allow for

the solving of x