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Math Help - Expected value calculation

  1. #1
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    Expected value calculation

    For the cdf, calculate the E[X^3 +1]
    F(x)=\left\{\begin{array}{cc}0&\mbox{ if }x< 0\\<br />
{1\over 4} x^2 & \mbox{ if } 0 \leq x \leq 2\\<br />
1 &\mbox{ if } x >2\end{array}\right.
    I get:
    E[X^3 +1]=E[X^3] +E[1]= \int_{0}^{2} x^3.{1 \over 2}xdx +1<br />
=\left[{x^5 \over 10}\right]^2_0 +1= {32 \over 10} +1 = {42 \over 10}
    is that correct?
    Last edited by mr fantastic; August 24th 2009 at 03:20 AM. Reason: Made square brackets larger.
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  2. #2
    Moo
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    Hello,

    yup, that's correct !

    however, you can simplify a bit... 42/10=21/5
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  3. #3
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    Quote Originally Posted by bigdoggy View Post
    For the cdf, calculate the E[X^3 +1]
    F(x)=\left\{\begin{array}{cc}0&\mbox{ if }x< 0\\<br />
{1\over 4} x^2 & \mbox{ if } 0 \leq x \leq 2\\<br />
1 &\mbox{ if } x >2\end{array}\right.
    I get:
    E[X^3 +1]=E[X^3] +E[1]= \int_{0}^{2} x^3.{1 \over 2}xdx +1<br />
=\left[{x^5 \over 10}\right]^2_0 +1= {32 \over 10} +1 = {42 \over 10}
    is that correct?
    Yes.
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