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Math Help - How to determine the transformation function between two given random variables

  1. #1
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    How to determine the transformation function between two given random variables

    Q: "If a random variable has the pdf : How to determine the transformation function between two given random variables-codecogseqn-1-.png find the transformation that would generate this random variable from the standard uniform."

    My approach is laid out below, but it's a fail since if I then try to use the transform function against an r.v. that's 'standard uniform' (ie: Y~U[0,1]), I'll generate the pdf for X as above just fine, but the interval is borked (ie: I don't get -1<= x <= 1). What am I missing here?

    How to determine the transformation function between two given random variables-latex.png<click image to enlarge to human-readable size>
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  2. #2
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    Re: How to determine the transformation function between two given random variables

    the limits on your left hand integral are incorrect. you need to integrate the pdf between -1 and x.

    ie, solve: \int_{-1}^x \frac{2+u}{4} du = y
    Last edited by SpringFan25; June 11th 2012 at 07:33 AM.
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