# Poisson Distribution
>[!Abstract] The Poisson Distribution is a form of [[Probability Distributions]] takes the following form:
>
>$f_X(x) = \frac{\lambda^x}{x!}e^{-\lambda} $
```R
# Probability x=4
dpois(x=4, lambda=7)
# P(X=0) & P(X=1) & ... & P(X=4)
dpois(x=0:4, lambda=7)
# P(X<=4)
sum(dpois(x=0:4, lambda=7))
# OR
ppois(q=4, lambda=7, lower.tail=T)
# P (X>=12)
ppois(q=12, lambda=7, lower.tail=F)
```