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