An R Introduction to Statistics

Poisson Distribution

The Poisson distribution is the probability distribution of independent event occurrences in an interval. If λ is the mean occurrence per interval, then the probability of having x occurrences within a given interval is:

x -λ f(x) = λ-e-- where x = 0,1,2,3,... x!

Problem

If there are twelve cars crossing a bridge per minute on average, find the probability of having seventeen or more cars crossing the bridge in a particular minute.

Solution

The probability of having sixteen or less cars crossing the bridge in a particular minute is given by the function ppois.

> ppois(16, lambda=12)   # lower tail 
[1] 0.89871

Hence the probability of having seventeen or more cars crossing the bridge in a minute is in the upper tail of the probability density function.

> ppois(16, lambda=12, lower=FALSE)   # upper tail 
[1] 0.10129

Answer

If there are twelve cars crossing a bridge per minute on average, the probability of having seventeen or more cars crossing the bridge in a particular minute is 10.1%.

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