Let X1, X2, . . . , Xn be i.i.d. random variables with E(X1) = 3. What is E(X1X2X3|X1)? (Simplify. Your answer should be a function of X1.)
The solution given is E(X1X2X3|X1) = X1E(X2X3|X1) = X1E(X2)E(X3) = 9X1.
However, I don't understand how to go from the first to second step. Isn't X1 a random variable and are we allowed to take it out like this?
My solution is E(X1X2X3|X1)=E(X1X2X3) = E(X1) E(X2) E(X3)= 3^3 = 27 which is not a function of X1.