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## #1 2009-08-31 05:04:21

Identity
Member
Registered: 2007-04-18
Posts: 934

### Changing the variables of a pdf

Say you have a pdf

and you have
(for example) and you wanted to find
, what does this change of variables actually achieve, and how are you meant to interpret the result? I've read over it but I don't really get the concept.

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## #2 2009-08-31 19:45:06

juriguen
Member
Registered: 2009-07-05
Posts: 59

### Re: Changing the variables of a pdf

Hi!

If you would like to understand HOW to calculate f(y), from Wikipedia [http://en.wikipedia.org/wiki/Probability_density_function]:

The probability contained in a differential area must be invariant under change of variables y = g(x)

This was for the simple case of a monotonic function g. There is a general expression in Wikipedia as well.

If you would like to know WHAT does it mean, I can only provide an example: Random Number Generation. Rather than explaining it myself, I think this other article will be useful [http://en.wikipedia.org/wiki/Inverse_transform_sampling]

Jose

Make everything as simple as possible, but not simpler. -- Albert Einstein

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