Expectation of X*Y= E(XY)

[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.

 

[blue_raver22]

Hello there,

Thank you for sharing your question about the expectation of X*Y. The expectation of a product of two random variables, X and Y, is defined as E(XY) = E(X)E(Y), where E(X) and E(Y) are the individual expectations of X and Y, respectively. In your case, since X and Y are dependent variables, their joint distribution needs to be considered in order to calculate E(XY). Without further information about the joint distribution, it is difficult to provide a specific answer. However, based on the given information of n=21 and Sum(x*y)= 1060.84, it seems like you might have the necessary data to calculate the covariance between X and Y, which can then be used to calculate E(XY). I would suggest consulting a statistics textbook or seeking help from a statistician for a more precise answer. Best of luck with your research!