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Math Help - Statistics help? Probability mass function p.m.f expected value?

  1. #1
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    Post Statistics help? Probability mass function p.m.f expected value?

    Let the p.m.f. (probability mass function) of X be de…noted by
    f(x) = 1 / x(x + 1) ; for x = 1, 2, 3,...

    1. Show that f is a p.m.f.
    2. What is E [X] in this case?

    Any help will be greatly appreciated!!!
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  2. #2
    MHF Contributor matheagle's Avatar
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    you need to show that this sums to one, and it does

    use partial sums to obtain

     {1\over x(x+1)} ={1\over x}-{1\over x+1}

    So  \sum_{x=1}^N {1\over x(x+1)} =\sum_{x=1}^N {1\over x} -{1\over x+1}= 1-{1\over N+1}\to 1

    as N\to\infty since this is a telescoping series

    The mean is infinite since that is a p-series (p=1)

    So E(X)=\sum_{x=1}^{\infty} {x\over x(x+1)} =\sum_{x=1}^{\infty} {1\over x+1}=\infty

    YOU can use the integral test and obtain \log N\to\infty

    but that's where the p-series comes from.
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    Last edited by Intsecxtanx; September 27th 2009 at 10:14 PM.
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  4. #4
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    I'm sorry, I didn't see that you wrote additional information. Thank you very much for the partial sums information!!!!!!
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  5. #5
    MHF Contributor matheagle's Avatar
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    I type 2 or 3 lines at a time and then I edit my TeX.
    There are plenty of typos and I need to edit it before I am done.
    Last edited by matheagle; September 28th 2009 at 07:29 AM.
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