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Topic:  Improper Integrals 
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Subject:  RE: Improper Integrals 
Author:  LFS 
Date:  Apr 5 2009 
Do they know statistics distributions? I like to do demonstrate these with
GeoGebra (freeware) and then prove them with improper/proper integrals.

I find it very interesting to show that a positive function is a pdf
(probability density functions) if it (improperly) integrates to 1 (full
probability).
Exponential distribution: f(x)=lambda*exp(lambda*x) for lambda>1 integrates
from 0 to infinity to 1. (e.g. lambda = 1.8). Nice easy improper integral.
Here, they can then play with proper integrals too such as: find x so that
Pr(X<x)=1/2  that is, when do you get half the probability and/or think both
about what this means with probability and/or halflife.
Exponential Polynomial distribution: f(x)=7.5*exp(3x)7.5exp(5x) which
is a typical distribution for "crash time" or "failure".
 
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