# Geometric Distribution >[!Abstract] The Geometric Distribution, is a form of [[Probability Distributions]] takes the following form: > >$ P(X = x) = (1-p)^{x-1} p $ > >This distribution is a special case of the negative [[Binomial Distribution]] and represents the probability of the number of Bernoulli trials needed before the first success. In the above formula $p$ is the probability of success > >![[geom_distribution.png]] > The geometric distribution is used to calculate [[Customer Lifetime Value — Survival Analysis|customer lifetime]] given customer churn rate that is constant over time. The quesiton is how many months it would take for the customer to churn? - The average customer lifetime is the expectation of the geometric distribution i.e. $1/c$ - On average, it takes $1/c$ months for a customer to churn - If c = 10% -> average customer lifetime is 10 months - If c = 20% -> average custoemr lifetime is 5 months