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Math Help - expectation and variance

  1. #1
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    expectation and variance

    say if X is the random variable, then
    then the expectation E[X] is the integration of x * pdf
    and the variance is the integration of x^2 * pdf - E[X]^2

    what if X^2 is the random variable?
    what is the expectation and variance?
    is Var [X^2] = integration of x^4 * pdf - E[X^2]^2?
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  2. #2
    MHF Contributor
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    i cant quite tell what you are trying to write.

    if  E(x) = \int x f(x) dx
    then
      E(g(x)) = \int g(x) f(x) dx

    so
    E(x^2) = \int x^2 f(x) dx
    E(x^4) = \int x^4 f(x) dx


    Finally,
    Var(x^2) = E((x^2)^2) - (E(x^2))^2
     = E(x^4) - (E(x^2))^2
    Last edited by SpringFan25; June 9th 2010 at 10:17 AM.
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  3. #3
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    haha sorry! that's what I meant!
    anyways, thanks for the clarification!
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