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Math Help - cumulative density function

  1. #1
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    cumulative density function

    i have f(x) = (a+1)x^a 0<x<1
    I need to find the cumulative density function.
    I have had an attempt but im not confident in my answer. It looks too easy!

    \int_0^x (a+1) t^a \, dt

    = (a+1) \int t^a \, dt

    = (a+1) \left[ \frac{t^{a+1}}{(a+1)}\right]_0^x

    = x^{a+1}.

    Does this look correct at all.
    Thanks
    sorry but i just could not get latex to work
    Last edited by mr fantastic; March 20th 2009 at 07:25 PM. Reason: That's OK, I could :)
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  2. #2
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    Quote Originally Posted by ben.mahoney@tesco.net View Post
    i have f(x) = (a+1)x^a 0<x<1
    I need to find the cumulative density function.
    I have had an attempt but im not confident in my answer. It looks too easy!

    \int_0^x (a+1) t^a \, dt

    = (a+1) \int t^a \, dt

    = (a+1) \left[ \frac{t^{a+1}}{(a+1)}\right]_0^x

    = x^{a+1}, {\color{red}0 < x < 1}

    Does this look correct at all.
    Thanks
    sorry but i just could not get latex to work
    This looks OK but is incomplete. I'd add the bit in red and also what I have below:

    F(x) = 0 for x \leq 0 and F(x) = 1 for x \geq 1.
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