Definition:
In statistics, poisson distribution is one of the discrete probability distribution.
This distribution is used for calculating the possibilities for an event with the given average rate of value(λ). A poisson random variable(x) refers to the number of success in a poisson experiment.
Formula:
f(x) = e-λλx / x!
where,
λ is an average rate of value.
x is a poisson random variable.
e is the base of logarithm(e=2.718).
Example:
Consider, in an office 2 customers arrived today. Calculate the possibilities for exactly 3 customers to be arrived on tomorrow.
Step1: Find e-λ.
where, λ=2 and e=2.718
e-λ = (2.718)-2 = 0.135.
Step2: Find λx.
where, λ=2 and x=3.
λx = 23 = 8.
Step3: Find f(x).
f(x) = e-λλx / x!
f(3) = (0.135)(8) / 3! = 0.18.
Hence there are 18% possibilities for 3 customers to be arrived on tomorrow.
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