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Poisson Distribution Formula

Poisson distribution is actually another probability distribution formula.  As per binomial distribution, we won’t be given the number of trials, or the probability of success on a certain trail. Average number of successes will be given in a certain time interval. The average number of successes is called as “Lambda” and denoted by the symbol “λ”.

The formula for Poisson Distribution formula is given below:

\[\large f\left(x\right)=\frac{e^{-\lambda}\:\lambda^{x}}{x!}\]

Here,

$\lambda$ is the average number
x is a Poisson random variable.
e is the base of logarithm.

Solved Examples

Question 1: As only 3 students came to attend the class today, find the probability for exactly 4 students to attend the classes tomorrow?

Solution:

Given,
Average rate of value($\lambda$) = 3
Poisson random variable(x) = 4

Poisson distribution=f(x) = $\frac{e^{-\lambda} \lambda^{x}}{x!}$

$=\frac{(2.718)^{-1}5^{7}}{7!}$

= 0.1045