Statistics & probability
Exponential waiting time
Estimate a waiting-time probability under a constant-rate model.
A clear answer. Here’s how.
For an exponential waiting time with rate λ, P(T>t)=exp(−λt), P(T≤t)=1−exp(−λt), mean=1/λ and median=ln(2)/λ. Uses expm1 for small cumulative probabilities. Assumes independent events and a constant rate; the time unit must match the rate.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Events per time unit
- 0.5
- Waiting time in the same time unit
- 3
Example result
- P(T ≤ time)
- 0.776869839852
- P(T > time)
- 0.223130160148
- Mean waiting time
- 2
- Median waiting time
- 1.38629436112