Exponential Distribution Calculator
Calculate P(X < x) = 1 - e^(-lambda * x).
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Enter the rate parameter (lambda) and the x value. The calculator computes P(X < x) using the cumulative distribution function 1 - e^(-lambda * x). It also shows the survival function P(X > x) and distribution statistics.
About This Calculator
The exponential distribution models the time between events in a Poisson process. If events occur at a constant average rate lambda, the waiting time between consecutive events follows an exponential distribution. It is memoryless: the probability of waiting another t units is the same regardless of how long you have already waited.
Frequently Asked Questions
What is the memoryless property?
The exponential distribution is the only continuous distribution with the memoryless property: P(X > s+t | X > s) = P(X > t). Past waiting time does not affect future probability.
How is it related to the Poisson distribution?
If events follow a Poisson process with rate lambda, then the time between events follows an exponential distribution with the same lambda.
What is the mean of the exponential distribution?
The mean is 1/lambda. If events occur 5 times per hour (lambda=5), the average waiting time is 1/5 = 0.2 hours = 12 minutes.