E [E [Y | X ]] = integral of E [Y | X] f (x) dx Can anyone explain explain the concept of multiplying f(x)?
You are computing expectation of a function of a random variable X with pdf f(x): E[g(x)] = integrate{ g(x) * f(x) dx } Here g(x) = E(Y | X = x) Check section 3.1 in page 125.