Exponential distribution: Difference between revisions
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imported>Michael Hardy |
imported>Michael Hardy |
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Let ''X'' be a real, positive stochastic variable with [[probability density function]] | Let ''X'' be a real, positive stochastic variable with [[probability density function]] | ||
: <math>f(x)= \lambda e^{-\lambda x} \ | : <math>f(x)= \lambda e^{-\lambda x}\,</math> | ||
Then ''X'' follows the exponential distribution with parameter <math>\lambda</math>. | for ''x'' ≥ 0. Then ''X'' follows the exponential distribution with parameter <math>\lambda</math>. | ||
==References== | ==References== | ||
Revision as of 18:41, 8 July 2007
The exponential distribution is any member of a class of continuous probability distributions assigning probability
to the interval [x, ∞).
It is well suited to model lifetimes of things that don't "wear out", among other things.
The exponential distribution is one of the most important elementary distributions.
A basic introduction to the concept
The main and unique characteristic of the exponential distribution is that the conditional probabilities P(X > x + 1) stay constant for all values of x.
More generally, we have P(X > x + s | X > x) = P(X > s) for all x, s ≥ 0.
Formal definition
Let X be a real, positive stochastic variable with probability density function
for x ≥ 0. Then X follows the exponential distribution with parameter .
