How this calculator works
Rate is the reciprocal of the mean waiting time. The survival probability declines exponentially. This memoryless model assumes a constant rate, so it does not describe ageing equipment with increasing hazard. Negative evaluation points have zero density and cumulative probability.
Formula
f(x) = λexp(-λx); F(x) = 1-exp(-λx); E[X] = 1/λ; Var[X] = 1/λ²; x_p = -ln(1-p)/λ.
Worked example
A rate of 2 per hour gives a mean wait of 0.5 hours. Waiting at most 0.5 hours has probability 1-exp(-1) = 0.6321206.
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Frequently asked questions
What unit does rate use?
The reciprocal of x. If x is hours, enter events per hour.
Is mean waiting time the same as median?
No. The median is ln(2)/λ, smaller than the mean.
How is this related to Poisson?
A constant-rate Poisson process has exponential times between events.