How to find E(XY) when X and Y are NOT indepdant?

  1. 1. The problem statement, all variables and given/known data

    I have a joint pdf f_{XY}(x,y) = (2+x+y)/8 for -1<x<1 and -1<y<1

    2. Relevant equations

    I have to work out E(XY) but I have previously worked out that X and Y are NOT independant (that is f_{XY}(0,1) doesn't equal f_X{0}*f_Y{1}). I am using maxima so I don't need help with any integration, I just need to know what formula because I've read that E(XY) = E(X)E(Y) only when they're indepdant... so what happens when they're not?
  2. jcsd
  3. You integrate xy against the pdf. Do you not have the textbook?
  4. No, there is no text book for this, I have bought some books, but none of them are written for people who aren't the best at statistics. I have no idea what you mean, isn't there an easier way using E(X) and E(Y) which I already have?
  5. No, there's not. Is this for a class?
  6. Oh goody double posting! Laura you now have two people telling you the same thing-- integrate. I don't know why you had to start two threads on the same topic instead of just being patient.
  7. You can use the definition of an expectation.
    E(XY) = [tex]\oint\oint[/tex]x*y*f(x,y) dy dx
    Or you could argue that since the function is symmetric about 0 and the intervals [-1, 1] are centred about 0 that E(XY) = 0
  8. statdad

    statdad 1,478
    Homework Helper

    The density isn't symmetric about zero.

    Laura, for any joint continuous distribution, whether or not [tex] X, Y [/tex] are independent, you can find [tex] E[XY] [/tex] as

    \iint xy f(x,y) \, dxdy
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