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Math Help - Moment generating function of piecewise pdf.

  1. #1
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    Moment generating function of piecewise pdf.

    I know that for a continuous, non-piecewise function, you can usually find the mgf(x,t) of f(x) by integrating, from minus infinity to infinity, (e^tx)*f(x)dx.

    But if given a piecewise function,
    eg
    g(x) = h(x) for 0<= x< infinity,
    = j(x) for - infinity < x <= 0,
    and h(0) = j(0)

    do I firstly integrate from 0 to infinity, (e^tx)*h(x)dx,
    then integrate from - infinity to 0, (e^tx)*j(x)dx,
    and then multiply or add the two resulting integrals together in order to get the mgf of g(x) ?

    I'm supposed to find the mean and variance after that, but I know how to do that once I know the mgf.
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  2. #2
    MHF Contributor matheagle's Avatar
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    You add, it's just an integral, you break up the integral into the three parts.
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