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Expected value of bivariate pdf

  1. May 8, 2009 #1
    Is the expected value E[x]or E[y] of a bivariate pdf fXY(xy)

    \int x f(x,y)dx

    or

    E[y]

    \int y f(x,y)dy ?

    example if f(x,y) = x+y

    E[X] = \int x *(x+y)dx


    regards
    Brendan
     
  2. jcsd
  3. May 9, 2009 #2

    mathman

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    Science Advisor
    Gold Member

    You need to carry out the double integral. A single integration gives the conditional expection of one variable with rexpect to the other.
     
  4. May 9, 2009 #3
    So just say you had the lmits of 0<x<1 0<y<1
    The expected value would be:
    [itex]
    E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy

    = 7/12
    [\latex]
    Is that right?
     
  5. May 9, 2009 #4
    Sorry,

    [itex]
    E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy

    = 7/12
    [/itex]

    regards
     
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