# 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