Exponential distribution: Difference between revisions
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imported>Michael Hardy m (typo) |
imported>Michael Hardy (→A basic introduction to the concept: This example is dubious. Cleaned up notation.) |
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==A basic introduction to the concept== | ==A basic introduction to the concept== | ||
The main and unique characteristic of the exponential distribution is that the [[conditional probability|conditional probabilities]] P(X>x+1 | The main and unique characteristic of the exponential distribution is that the [[conditional probability|conditional probabilities]] P(''X'' > ''x'' + 1) stay constant for all values of ''x''. | ||
More generally, we have P(X>x+s | More generally, we have P(''X'' > ''x'' + ''s'' | ''X'' > ''x'')= P(''X'' > ''s'') for all ''x'', ''s'' ≥ 0. | ||
===Formal definition=== | ===Formal definition=== | ||
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} \mbox{ for }x > 0. </math> | |||
Then ''X'' follows the exponential distribution with parameter <math>\lambda</math>. | |||
==References== | ==References== | ||
Revision as of 18:40, 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
Then X follows the exponential distribution with parameter .
