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Bookmark or Share- What does $E [XY]$ mean? - Mathematics Stack ExchangeStack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
- probability theory - Intuition behind $E(XY) = E(X) E(Y) $ for ...Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
- probability - Expectation E(XY) of two dependent variables ...1. What you need is the joint distribution of (X, Y) (X, Y). Then e.g. in discrete case EXY =∑x,y xyP(X = x, Y = y) E X Y = ∑ x, y x y P (X = x, Y = y). If there is a PDF then EXY = ∫ xyfX(x, y)dxdy E X Y = ∫ x y f X (x, y) d x d y (both under condition that the expectation exists, of course). In your example we are dealing with the ...
- Proof of $ E (XY) = E (X) E (Y) - E(XY) = E(X) E(Y) $ - Mathematics ...Using our expression we just computed for P(XY = z), we substitute. E(XY) = ∑ z ∈ T∑ x ∈ SzP(X = x)P(Y = z / x). Note that if z / x is not in our set S, P(Y = z / x) = 0, so we may simplify the above summation to. E(XY) = ∑ z / x ∈ S∑ x ∈ SzP(X = x)P(Y = z / x). Now make the substitution y = z / x.
- probability - E(XY) = E(X)E(Y) - Mathematics Stack Exchange$\begingroup$ First, handle the finite case using the theorem. Then handle the infinite case, but be careful to properly distinguish infinite from non-existent expectations (remember that for Lebesgue integrals, it only makes sense to assign $+\infty$ or $-\infty$ to an integral if only either the positive or the negative part diverges!).
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