Expectation of X*Y= E(XY)

  • Thread starter James1990
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  • #1
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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.
 

Answers and Replies

  • #2
mathman
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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.
 
  • #3
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Expectation doesn't require independence so you can just do E(xy)=E(x)*E(y) or in this case, sum(XY)/n
 
  • #4
mathman
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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.
 
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