Poisson Distribution Formula

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. The average number of successes will be given in a certain time interval. The average number of successes is called “Lambda” and denoted by the symbol “λ”.

The formula for Poisson Distribution formula is given below:

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

Here,

\(\begin{array}{l}\lambda\end{array} \)
 is the average number
x is a Poisson random variable.
e is the base of logarithm and e = 2.71828 (approx).

Solved Example

Question: 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(

\(\begin{array}{l}\lambda\end{array} \)
) = 3
Poisson random variable(x) = 4

Poisson distribution = P(X = x) =

\(\begin{array}{l}\frac{e^{-\lambda} \lambda^{x}}{x!}\end{array} \)

\(\begin{array}{l}\begin{array}{c}P(X = 4)=\frac{e^{-3} \cdot 3^{4}}{4 !} \\ \\P(X = 4)=0.16803135574154\end{array}\end{array} \)

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