The Exponential Distributions

Next: Relationship with the Poisson Distribution
Previous: Normal Distribution as an Approximation

The Exponential Distribution

Widely used in science / engineering, this family has a single parameter l >0 with the following pdf:

For any positive l, the p.d.f. has a value of l at x=0 and as x becomes larger the pdf quickly starts to become asymptotic with the x-axis and approaches a value of 0 as x approaches ¥.

The expected value and variance of X are given by

The cumulative distribution function is easily computed as:

Thus

Pr(a£X£b) =

Note that this is the same as F(b)-F(a)...

ENGR 0020 Home Page

Next: Relationship with the Poisson Distribution
Previous: Normal Distribution as an Approximation

Jayant Rajgopal