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Transformation of non-monotonic density functions

  1. Jul 11, 2006 #1
    What's the general way to solve them?
    I know that the thm which states:
    f(y) = f(g(y)) * |D g(y)| is not applicable, since it is only applicable to strictly increasing or decreasing functions.

    here's a sample question: Let X have the density function f(x) = 1/2 for -1<x<1, 0 otherwise. Let Y = X + 1 for 0<x<1 and Y = -2X for -1<x<0. Find the density function of Y.

    If I use the above forumule, the domains for Y = X+1 and Y =-2X would intersect while having different density functions...so I'm not sure what to do there.

  2. jcsd
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