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Math Help - How do I find the mean of this?

  1. #1
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    How do I find the mean of this?

    I have \mathbb{E}[X]=\mu

    <br />
f(x) = \left\{<br />
\begin{array}{lr}<br />
2x^2 + x, & x \leq \mu\\<br />
x^2 + 3x + 1, & x \geq \mu<br />
\end{array}<br />
\right.<br />

    How do I find \mathbb{E}[f(X)]?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by MMath09 View Post
    I have \mathbb{E}[X]=\mu

    <br />
f(x) = \left\{<br />
\begin{array}{lr}<br />
2x^2 + x, & x \leq \mu\\<br />
x^2 + 3x + 1, & x \geq \mu<br />
\end{array}<br />
\right.<br />

    How do I find \mathbb{E}[f(X)]?
    You don't have enough information to do any thing but write the expectation as an integral:

     <br />
E(f(X))=\int_{-\infty}^{\infty} f(x) p(x)~dx=\int_{-\infty}^{\mu}(2x^2 + x) p(x)~dx +<br />
\int_{\mu}^{\infty}(x^2 + 3x + 1) p(x)~dx<br />

    where p(x) the density of X.

    CB
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  3. #3
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    Hmmm... what if I also have the variance below the mean and the variance above the mean? Any better?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by MMath09 View Post
    Hmmm... what if I also have the variance below the mean and the variance above the mean? Any better?
    Depending on what exactly you mean by those may-be.

    CB
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