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Moment Generating Function

  1. Jan 21, 2010 #1
    Say r.v. X, we have pdf f(x) and mgf Mx(t) defined.

    Then define Y=-X, y is negative x.

    Can we get mgf of Y, i.e. My(t) and how?

    I know I can go the way to get pdf f(y) first then My(t). I want to know if Mx(t) is already in my hands, it should be easier to get My(t) other than do f(y) first.

    I thought about this whole afternoon. Just don't get it. Please help and thanks in advance.

  2. jcsd
  3. Jan 22, 2010 #2


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    Homework Helper

    Remember that for any random variable

    M_x(t) = E[e^{tx}]

    If you want the mgf for cX (any constant times X)

    M_{cX}(t) = E[e^{t(cx)}]

    How can you simplify this expression, how does it relate to [tex] M_X(t)[/tex],
    and how do both observations relate to your problem?
  4. Jan 22, 2010 #3
    I have found one way.

    I have here x=log(1-x) and f(x) also known.

    So we can see if I put x=log(1-x) in to Mcx(t), it can be simplified easily. Here is my solution for this problem and it depends on the form of function of x.
  5. Jan 22, 2010 #4


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    How does your second post relate to your first question?
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