We have 10 cards numbered from 1 to 10. We pick two cards among them. What is the expected value of the product of these two cards with and without replacement?
My thought: Let X and Y be the number on the two card For with replacement, X and Y are independent, so E(X*Y)=E(X)*E(Y)=30.25
For without replacement, since X and Y are dependent, I feel it is the same, but could not think a nice way to prove it. Thanks!