Kostenloser Exponential Verteilung Rechner

Berechnen Sie exponential distribution PDF und CDF. Model waiting times between events mit this kostenloser Rechner.

PDF f(x)

0.11156508

CDF P(X <= x)0.77686984
P(X > x)0.22313016
Mean (1/lambda)2.0000

PDF f(x) vs Rate Parameter (lambda)

Formel anzeigen →

Formel

## 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).

Lösungsbeispiel

Buses arrive at a rate of 0.5 per minute. What is the probability of waiting at most 3 minutes?

  1. 01lambda = 0.5, x = 3
  2. 02PDF: f(3) = 0.5 * e^(-0.5*3) = 0.5 * e^(-1.5) = 0.5 * 0.2231 = 0.1116
  3. 03CDF: P(X <= 3) = 1 - e^(-1.5) = 1 - 0.2231 = 0.7769
  4. 04P(wait > 3 min) = e^(-1.5) = 0.2231
  5. 05Mean waiting time = 1 / 0.5 = 2 minutes