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Math Help - discrete distribution - find the constant

  1. #1
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    Question discrete distribution - find the constant

    This is a question from Degroot and Schervish's Probability and Statistics Textbook: p 103 qn 9

    Suppose that a random variable X has a discrete distribution with the following probability function:

    f(x) = ( c/(x squared) for x=1,2,...
    ( 0 otherwise

    Find the value of the constant c.

    I tried working it out and my answer is c = 1.
    But the back of the textbook states the answer as 6 / pi squared.
    Please could someone help me understand why?
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  2. #2
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    Well, this is a well known sum: \sum\limits_{x = 1}^\infty  {\frac{1}{{x^2 }}}  = \frac{{\pi ^2 }}{6}.
    Does that help you understand?
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  3. #3
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    Thank you! I'd be interested to read the proof if that's possible.
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  4. #4
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    Quote Originally Posted by math beginner View Post
    Thank you! I'd be interested to read the proof if that's possible.
    It's a routine result using the Fourier Series for f(x) = x^2.
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