Solution
= Solution
The binary <regression function>[regression functions] are the <conditional class probabilities>
$$
\eta_1(x)=\mathbb P(Y=1\mid X=x)=\mathbb E(Y\mid X=x),
\qquad
\eta_0(x)=1-\eta_1(x).
$$
Under zero-one loss, the <Bayes classifier> is
$$
C^*(x)=\mathbf1_{\{\eta_1(x)\geq1/2\}},
$$
with arbitrary tie breaking. Its <Bayes decision boundary> is
$$
\{x:\eta_1(x)=\eta_0(x)\}
=\{x:\eta_1(x)=1/2\}.
$$