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Math Help - Relationship with the expectation value

  1. #1
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    Relationship with the expectation value

    In a recent homework question I was asked to find the followings:

    E(X)and \int_{0}^{\infty}[1-F_X(x)]dx
    F_X(x)=P(X\leq x)=\left\{\begin{matrix}<br />
(1-1/x^2) \  \  if \  \  x\geq 1\\ <br />
0 \  \ elsewhere<br />
\end{matrix}\right.

    This was easy, I found both to be 1. What bothered me was an remark that the prof made at the end of the question: he wrote "This is not a coincidence."

    Is this always true? Are there any proofs? Does it depend of F_X(x)? What has the expectation got to do with \int_{0}^{\infty}[1-F_X(x)]dx? I though the expectation is just like taking an average.
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  2. #2
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    Quote Originally Posted by synclastica_86 View Post
    In a recent homework question I was asked to find the followings:

    E(X)and \int_{0}^{\infty}[1-F_X(x)]dx
    F_X(x)=P(X\leq x)=\left\{\begin{matrix}<br />
(1-1/x^2) \ \ if \ \ x\geq 1\\ <br />
0 \ \ elsewhere<br />
\end{matrix}\right.

    This was easy, I found both to be 1. What bothered me was an remark that the prof made at the end of the question: he wrote "This is not a coincidence."

    Is this always true? Are there any proofs? Does it depend of F_X(x)? What has the expectation got to do with \int_{0}^{\infty}[1-F_X(x)]dx? I though the expectation is just like taking an average.
    Read this thread: http://www.mathhelpforum.com/math-he...pectation.html
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