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Joint Pdf Expected Value

  1. Apr 29, 2014 #1
    1. The problem statement, all variables and given/known data

    two random variables have a join pdf
    f(x,y)= c , x^2+y^2<= 1, x >0, y>0
    0, otherwise
    Find c.
    Find E{xy}.

    2. Relevant equations



    3. The attempt at a solution
    For the first part, since area= pi/4,
    c(pi/4) = 1
    c=(4/pi)
    b)
    x=cos θ
    y= sin θ
    ∫∫-(sin θ)^2(cos θ)^2 dθ dθ = -308. (integral from 0 to pi/2 for both bounds)
    This doesn't make sense to me. x,y are always positive how is the expected value negative? Am I doing something wrong?
     
  2. jcsd
  3. Apr 30, 2014 #2

    LCKurtz

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    You need ##x=r\cos\theta,~y=r\sin\theta,~dydx=rdrd\theta##. And where did that minus sign come from anyway?
     
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