Hi all In CT3-10 page 23, the penultimate line reads "= var[g] + 0 + bias^2 ..." Why is the middle term 0 ? Thanks
Hello Howard, The middle term is \(0\) because the middle term corresponds to the expression \(\mathbb{2(E[g]-\theta)E[g - E[g]]}\) which can be simplified as follows \begin{align} \mathbb{2(E[g]-\theta)E[g - E[g]]} &= \mathbb{2(E[g]-\theta)(E[g]-E[E[g]])} \\ &= \mathbb{2(E[g]-\theta)(E[g]-E[g])} \\ &= \mathbb{2(E[g]-\theta)\times0} \\ &= 0 \end{align} For the second step I have used the fact that the expected value of a constant is the constant itself. So, \(\mathbb{E[E[g]] = E[g]}\) Hope this helps. Regards, Kaustav.
