How Do You Calculate E(XY) for Dependent Variables with Given Observations?

[James1990]

Hi everyone,

I was searching an answer for E(XY), where X and Y are two dependent random variables, number of observations n=21 and Sum(x*y)= 1060.84. Can somebody help me?

It's not mentioned, but I think that each x and y of the distributions have the same probability to occur.
Thank you.

 

[mathman]

Since you don't know anything about X and Y individually, you could think in terms of Z=XY. Then the estimate for E(Z) = 1064.84/21.

 

[randomafk]

Expectation doesn't require independence so you can just do E(xy)=E(x)*E(y) or in this case, sum(XY)/n

 

[mathman]

Expectation doesn't require independence so you can just do E(xy)=E(x)*E(y) or in this case, sum(XY)/n

This statement is misleading, E(XY) may not = E(X)E(Y) if they are dependent. However in the problem stated here, nothing in particular is known about X and Y, only the product, so E(X) and E(Y) are irrelevant.