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Variance of square of random variable

  1. Jun 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Lets say I roll 2 fair dice and take the sum of the square of each dice. What formula will be the variance?

    2. Relevant equations
    var(x)=e(x^2)-e(x)^2


    3. The attempt at a solution
    For dice A;
    E(A)=3.5
    E(A^2)=91/6
    ^ same for dice B.

    VAR(A^2+B^2)=E(A^4)-E(A^2)^2+E(B^4)-E(B^2)^2 ?
     
  2. jcsd
  3. Jun 20, 2011 #2

    lanedance

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    how did you get to that? I'd start from
    [tex] var(A^2+B^2) = E((A^2+B^2)^2) - E((A^2+B^2))^2[/tex]

    and simplify from there, though you'll probably end up at a similar place you need to justify it
     
  4. Jun 21, 2011 #3
    well since i am throwing two different dice and squaring them, this means that they are independent, shouldnt I be able to use var(x+y)=var(x)+var(y)?

    VAR(A^2+B^2)=E(A^4)-E(A^2)^2+E(B^4)-E(B^2)^2
     
  5. Jun 21, 2011 #4

    lanedance

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    yep, you just need to mention your assumptions, you can also say the expectation values will be the same for A & B
     
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