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Math Help - MGF of gamma distribution

  1. #1
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    MGF of gamma distribution

    Hi all
    I am new here

    I just dont understand how to get the moment generating function of gamma distribution wit pdf:
    f(x;α,λ) = [λ^αx^(α−1)e^−λx]/Γ(α) , x ≥ 0; α,λ > 0.

    can anybody help me plz asap

    thanks alot
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  2. #2
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    Quote Originally Posted by ma19sa View Post
    Hi all
    I am new here

    I just dont understand how to get the moment generating function of gamma distribution wit pdf:
    f(x;α,λ) = [λ^αx^(α−1)e^−λx]/Γ(α) , x ≥ 0; α,λ > 0.

    can anybody help me plz asap

    thanks alot
    Where are you stuck? The problem boils down to calculating \int_0^{+ \infty} e^{-x( \lambda - t)} x^{a - 1} \, dx which in turn boils down to calculating \int_0^{+ \infty} e^{-y} y^{a - 1} \, dy and this is a well known integral ....
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