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This question already has an answer here:

To be more specific: Let the random variable X be distributed according to probability density function f(x). Then the pdf of Y=1/X is given by g(y)=1/y^2 f(1/y), see wikipedia.

I wonder if there is any citable reference for that. Or is it common knowledge? I'm coming from a different field of mathematics and lack some background in statistics. I looked through some text books, but didn't find any mention of it yet.

Thanks a lot!

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marked as duplicate by whuber Oct 5 '13 at 16:13

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ The duplicate does not provide references because this is an extremely well-known relationship that can be found in any textbook that covers distribution functions (at least any that assumes some basic Calculus knowledge of its readers). $\endgroup$ – whuber Oct 5 '13 at 16:14
  • $\begingroup$ It's just standard change of variable. Easiest way to see it is by beginning with $P(Y\leq y)=P(1/X \leq y) =...$ (taking great care with the case where $X$ can be zero). The case where $X>0$ is simple, perhaps try it first. Once you have the cdf, take the derivative to get the density. As whuber says, it's in pretty much any standard text that covers this stuff. $\endgroup$ – Glen_b Oct 6 '13 at 1:03