# 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) ```