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Math Help - Compute E[X]

  1. #1
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    Compute E[X]

    Compute E[X] if X has a probability density function given by
    f(x) = \begin{cases} c(1-x^2) & -1<x<1 \\ 0 & otherwise \end{cases}

    ---------------------------------My work ---------------------------------

    E[X] = \int_{-1}^{1} x. f(x) dx = \int_{-1}^{1} x . [c (1-x^2)]dx = ......=0.........Is this correct????
    Last edited by mr fantastic; December 29th 2009 at 11:22 PM. Reason: Improved some latex
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  2. #2
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    Hi zorro, first find c by saying

     \int_{-1}^{1} c(1-x^2) dx = 1

     c\int_{-1}^{1} (1-x^2) dx = 1

    To make things easier you can use some symmetry

     2c\int_{0}^{1} (1-x^2) dx = 1
    Last edited by pickslides; December 29th 2009 at 07:34 PM. Reason: *sp
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  3. #3
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    i am getting c = \frac{3}{4}............Is that right????

    what should i do now??????
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  4. #4
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    Quote Originally Posted by zorro View Post
    i am getting c = \frac{3}{4}............Is that right????

    what should i do now??????
    Now calculate \frac{3}{4}\int_{-1}^{1} x (1 - x^2) \, dx = \frac{3}{4} \int_{-1}^{1} x - x^3 \, dx . Since the integrand is odd, the integral is equal to zero (which is what you had in the first place).

    Note that the value of c is irrelevant for this particular calculation. But it might be needed for other calculations ....
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  5. #5
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    thanks my fantastic and pickslides
    cheers
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