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Math Help - going from distribution to density function

  1. #1
    Junior Member
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    going from distribution to density function

    Suppose that a random variable
    X has distribution function


    F
    (x):


    1-(1+x)exp(-x) - (x > 0)

    0 - (
    x <0)


    (a) Find the density function of
    X.

    (b) Find the mean and variance of X.

    Could anyone please go through this in steps please. I know the theory but havn't seen a practical example. Thanks alot!
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  2. #2
    MHF Contributor
    Joined
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    Here is the first part

    1)
    To find the dessity function, differenciate the distribution function.

    f(x) = \frac{dF}{dx} = 0 - \left( 1*e^{-x}  + (-1)e^{-x}(1+x) \right)

    f(x) = \frac{dF}{dx} = 0 - \left( e^{-x}  + (-1-x)e^{-x} \right)

    f(x) = \frac{dF}{dx} = -e^{-x}  + (1+x)e^{-x} \right)

    provided that x>0

    f(x) = 0 otherwise.

    b)

    To find the mean of x, do the integral:

    E(X) = \int_0^\infty x * f(x)

    can you post as much as you can do?
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  3. #3
    Junior Member
    Joined
    Aug 2010
    Posts
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    I've got up to that point before. I managed to get same answer as you for part a)
    but my answer for part b) always seems over complicated. I get a lot of complicated integrating and with the answer i get, it's always equal to 0.
    I'm not sure what i'm doing wrong.
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