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Math Help - Gamma Distribution Help!!

  1. #1
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    Gamma Distribution Help!!

    Suppose the reaction time X of a randomly selected individual to a certain stimulus is a standard gamma distribution with (alpha=2)


    What is F(5;2) using gamma

    show steps i dont understand!
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  2. #2
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    I'm guessing by standard gamma they mean the scale parameter (i.e. beta) is equal to 1. Since alpha = 2, we can just write down the density f_X (x) = \frac{1}{\Gamma(2)} x^{2 - 1}e^{-x} = xe^{-x}. You can solve for F(x) in the usual way using integration by parts. If you haven't had calculus, or are just being blindsided by this (since this is the pre-university forum), just post so and I'll give a different explanation (at some point, I have to go to class).
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  3. #3
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    you put 2 in for x, but didnt put 2 in for e^-x
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  4. #4
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    Nah, I put in 2 for alpha everywhere. Or are you talking about the exponential not having a parameter? That is where beta would normally be, but since it's 1, it's just e^{-x}. Just to be sure we're clear, the density for a Gamma(alpha, beta) is f(x) = \frac{1}{\Gamma(\alpha) \beta^{\alpha}} x^{\alpha - 1} e^{\frac{-x}{\beta}}. Plug 1 for beta and 2 for alpha and you get the density I posted.
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  5. #5
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    can u show in steps the function evaluated at F(5;2)

    its supposed to equal
    .960
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  6. #6
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    To get F(5), use the fact that F(x) = \int_0 ^{x} f(t)dt. I did this and got .960. After integration by parts you get F(x) = 1 - e^{-x}(x + 1)
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