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Expected value equation

  1. Mar 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Let x and y be independent random variables with E[x]=1, E[y]=-1, var[x]=1/2, var[y]=2
    Calculate E[(x+1)2(y-1)2]


    2. Relevant equations

    E[x]=1=μ
    E[y]=-1=μ
    var[x]=1/2 =E[(x-μ)2]
    var[y]=2=E[(x-μ)2]




    3. The attempt at a solution

    Since x and y are independent,
    E[(x+1)2(y-1)2]=E[(x+1)2]*E[(y-1)2]

    var[x]=1/2=E[(x-1)2]

    var[y]=2=E[(y+1)2

    The signs in the equation I need to solve are throwing me off. I feel like I'm missing something simple. Any help is appreciated!
     
  2. jcsd
  3. Mar 11, 2014 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Sometimes the easiest approach is to use the standard result
    [tex] \text{Var}(Y) = E(Y^2) - (E Y)^2,[/tex]
    which is true for any random variable having finite mean and variance. (At some point in your life, you should prove it.) You can expand out ##(Y-1)^2## and go on from there.
     
  4. Mar 11, 2014 #3
    Thanks Ray!

    Thank you for the hint! Does this look right?

    E[(x+1)2]*E[(y-1)2]

    =(E[X2]+2E[X]+E[1])(E[Y2]-2E[Y]+E[1])

    =(Var[X]+E[X]2+2E[X]+E[1])(Var[Y]+E[Y]2-2E[Y]+E[1])

    =(.5+1+2+1)(2+1+1+1)=18
     
    Last edited: Mar 11, 2014
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