Exponential Distribution
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Calculate
Example: on average, 3 customers an hour arrive at a counter. What is the chance that the next one arrives within half an hour (x = 0.5)? Change the values to work out your own case.
Step by step
What each term means
- Density (f(x))
- The height of the curve at x, for x ≥ 0. It is not a probability: probabilities are areas under the curve, such as P(X ≤ x) = 1 − e^(−λx).
- Rate (λ)
- How many events happen, on average, per unit of time or distance. The mean wait between them is 1/λ: with 3 customers an hour, 20 minutes.
- Exponential Decay (e^(−λx))
- The chance of getting past x with no event, P(X > x). It drops by the same fraction for each extra unit of waiting — hence the distribution's lack of memory.