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Math Help - mean value from a CDF

  1. #1
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    mean value from a CDF

    Hi, I'm not sure if this post is in the right place, but it's a university level question anyhow...

    Random variable X has a cumulative distribution function (CDF) given by:
    F_{X}(x) = \left\{\begin{matrix}0\; \; \; \; x\leqslant 0\\ x/2\; \; \; \; x\,\epsilon \: (0,2)\\1\; \; \; \; x\geq2\end{matrix}\right.

    What is its mean value?

    I'd seriously appreciate some help on this one - I'm not statistically minded at all and I'm finding the whole pdf cdf thing really confusing.

    Cheers and thanks in advance!

    Rorosingsong
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  2. #2
    MHF Contributor matheagle's Avatar
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    Re: mean value from a CDF

    this is a uniform (0,2)
    Hence the mean is 1
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  3. #3
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    Re: mean value from a CDF

    Hi matheagle!

    Thanks for your prompt reply, but I'm new to stats and not sure of what you mean by a "a uniform (0,2)"...

    Could someone explain the working to me? I know it involves integrating FX(x), but I don't understand why x smaller than or equal to 0 or x larger than or equal to 2 aren't involved...

    Thanks,
    rorosingsong
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  4. #4
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    Re: mean value from a CDF

    Quote Originally Posted by rorosingsong View Post
    Hi matheagle!

    Thanks for your prompt reply, but I'm new to stats and not sure of what you mean by a "a uniform (0,2)"...

    Could someone explain the working to me? I know it involves integrating FX(x), but I don't understand why x smaller than or equal to 0 or x larger than or equal to 2 aren't involved...

    Thanks,
    rorosingsong
    The pdf is given by dF/dx, from which what is said in post #2 should be obvious. If it's not obvious, then use the the pdf and the definition of mean to do the calculation directly.
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  5. #5
    MHF Contributor matheagle's Avatar
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    Re: mean value from a CDF

    Your book should have the uniform density in it.
    It's the most basic continuous density.
    Otherwise google it and
    http://en.wikipedia.org/wiki/Uniform...on_(continuous)
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