Free Exponential Distribution Calculator
Calculate the probability density and cumulative probability for the exponential distribution, which models time between independent events.
PDF f(x)
0.11156508
PDF f(x) vs Rate Parameter (lambda)
How to Calculate Exponential Distribution Probabilities
Formulas
PDF: f(x) = lambda * e^(-lambda*x) for x >= 0
CDF: P(X <= x) = 1 - e^(-lambda*x)
The exponential distribution models the time between events in a Poisson process. The parameter lambda is the rate (events per unit time). The mean waiting time is 1/lambda. It has the memoryless property: P(X > s+t | X > s) = P(X > t).
Example Calculation
Buses arrive at a rate of 0.5 per minute. What is the probability of waiting at most 3 minutes?
- 01lambda = 0.5, x = 3
- 02PDF: f(3) = 0.5 * e^(-0.5*3) = 0.5 * e^(-1.5) = 0.5 * 0.2231 = 0.1116
- 03CDF: P(X <= 3) = 1 - e^(-1.5) = 1 - 0.2231 = 0.7769
- 04P(wait > 3 min) = e^(-1.5) = 0.2231
- 05Mean waiting time = 1 / 0.5 = 2 minutes
Frequently Asked Questions
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