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Moment generating function help?

  1. May 11, 2010 #1
    I know that hte MGF is = the E[e^tx]

    How do i show that if i take a sample (X1;X2; : : :Xn) from the exponential density f(x) = A*e^(-Ax), then the sum Z = sum(Xi) has the gamma density?

    I found that the MGF for the exponential was A/(t-A) if that helps

    Thanks
     
  2. jcsd
  3. May 12, 2010 #2

    statdad

    User Avatar
    Homework Helper

    Note that

    [tex]
    e^{t\sum X_i}} = \prod{e^{tX_i}}
    [/tex]

    This will relate the form of the mgf of the sum to the individual mgfs of the sample.
     
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