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Can anybody help me with this (statistics)?

  1. Dec 11, 2012 #1
    Let X be [tex]\Gamma(3.5,2)[/tex]. Find [tex]E(X^3)[/tex].

    We can't write E(X^3)=E(X)E(X)E(X), right? (since they are not independent)...

    So I just tried to compute:

    [tex]E(X^3) = int_0^{/infty} \frac{x^3}{\Gamma(3.5)2^{3.5}} x^{3.5-1} e^{-x/\beta} dx[/tex]

    But I'm having a problem, since [tex]\Gamma(3.5) = (3.5)![/tex] and I don't know how to compute (3.5)!...

    Thanks in advance
     
  2. jcsd
  3. Dec 11, 2012 #2

    Ray Vickson

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    ##x^3 x^{3.5 - 1} = x^{6.5 - 1}, ## so after supplying the appropriate factors you essentially have ##X^3 \Gamma(3.5,2) = c \Gamma(6.5,2)## for some constant c.
     
  4. Dec 11, 2012 #3
    Thanks, but I don't understand how you got this equality...
     
    Last edited: Dec 11, 2012
  5. Dec 11, 2012 #4

    Ray Vickson

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    What I really meant (but it was harder to write) was: if f1(x) = probability density of Gamma(3.5,2) and f2(x) = probability density of Gamma(6.5,2), then we have x^3*f1(x) = c*f2(x) for some constant c. Now I will leave the rest up to you.
     
  6. Dec 11, 2012 #5
    Ok, thanks... :)
     
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