Exponential Distribution Calculator
Calculate cumulative probability, survival probability, density and mean for a nonnegative waiting time with constant rate.
Formula
F(x)=1−e^(−λx); S(x)=e^(−λx); f(x)=λe^(−λx); mean=1/λ
P(X ≤ x) ≈ -expm1(-(2)×(1)) · P(X > x) ≈ exp(-(2)×(1)) · Probability density ≈ (2)×(0.1353352832) · Mean (chosen unit) ≈ 1÷(2)
How to use
- Enter a positive rate λ.
- Enter x in the corresponding time unit.
- Read probabilities, density and mean.
Examples
- λ=2 and x=0 give F=0, S=1 and mean=0.5.
Frequently asked questions
What units should I use?
For λ per hour, enter x in hours; the mean is then in hours.
Is density a probability?
No. Density can exceed 1; an exact value has probability zero.
Which model is assumed?
A continuous exponential waiting time with constant rate and no location shift.
Sources
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