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

by laura_a
Tags: indepdant
 P: 61 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
 P: 491 You integrate xy against the pdf. Do you not have the textbook?
 P: 61 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?
P: 491

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

No, there's not. Is this for a class?
 P: 352 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.
 P: 2 You can use the definition of an expectation. E(XY) = $$\oint\oint$$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
 HW Helper P: 1,344 The density isn't symmetric about zero. Laura, for any joint continuous distribution, whether or not $$X, Y$$ are independent, you can find $$E[XY]$$ as $$\iint xy f(x,y) \, dxdy$$

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