# exponential distribution

## 1. geometric distribution

- There is an interpretation of the geometric distribution as the probability of seeing \(k\) failures before the first success
- \(P(X=k) = (1-p)^kp\)

## 2. exponential distribution

- In the limit, as we make the time windows smaller, we have the continuous time analogue of the geometric distribution, which is the expontial distribution:
- \(f(x;\lambda) = \lambda e^{-\lambda x}\), \(x\geq 0\)
- see math overflow

## 3. note

- consider the same way that the poisson distribution is the continuous analogue of the binomial distribution