Exponential Distribution Calculator
Models the wait until the next event when events happen independently at a steady rate.
P(X ≤ x), event by this time
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P(X > x), still waiting —
Density at x —
Mean wait —
Median wait —
Standard deviation —
Reading this —
The formula
P(X ≤ x) = 1 − e^(−λx) mean = 1 ÷ λ, median = ln 2 ÷ λ
It describes the wait between events in a Poisson process. The units of x and λ must match.
What to watch out for
The mean is pulled up by the occasional long wait, so more than half of all waits are shorter than the mean.
Frequently Asked Questions
What is a worked example?
With an average of one event every 2 hours, the chance of one within 3 hours is 0.77687.
What share of waits are shorter than the mean?
63.21%, whatever the rate.