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Hi everyboy,
I have a question for which I have tried to solve about 10 days.
The question is:
Given X and Y 2 independent random variables, with the expectation respectively E(X) and E(Y).
Given h(X) a function of X , h(X) = X
Given g(Y) a function of Y, g(Y) = Y
Given k(X,Y) a function of X and Y, k(X,Y) = XY+(1-X)(1-Y)
Main question: What is the expectation of the function: h(X) * g (Y) * 1/k(X,Y) ? ( E[h(X) * g (Y) * 1/k(X,Y)] = ?) in term of E(X) and E(Y)
I have researched around on some textbooks and on the internet, what i have found:
1/ E(X+Y) = E(X) + E(Y)
2/ E[XY] = E(h(X)) * E(g(Y)) if X and Y are independent
I dont know that if E[hX*gY*kXY] = E(hX)*E(gY)*E(kXY) ??? I hope it is TRUE, but I dont think that it is TRUE, because h and g are independent, but h and k (or g and k) are NOT independent.
Thank you if you can help me with this pb!
Java.
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