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Thread: Deriving MGF for exponential

  1. #1
    Actuary.com - Level I Poster
    Join Date
    Nov 2007
    Posts
    20

    Deriving MGF for exponential

    I understand that M(t) = E[e^tX]

    so for example, for exponential with mean 1/c would be

    integral (0, inf) e^tx * ce^-cx dx

    which simplifies to

    c * integral (0, inf) e^x(t-c) dx

    but how do we know whether (t-c) < 0 or not?

    Thanks in advance.

  2. #2
    Actuary.com - Level II Poster lee_onion's Avatar
    Join Date
    Dec 2007
    Posts
    30
    If t >= c, then the integral may be INF, and that means the MGF is not exist.
    And when t < c, the MGF exists and it equal to c/(c-t).

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