Understanding the Expression of Expected Prediction Error (EPE) from "The Elements of Statistical Learning" (Page 26, Equation 2.27)

Question

The expression comes from The Elements of Statistical Learning p26(2.27).

Following picture is our tearcher's slide:

I don't understand the red underlined. Isn't that the expectation of $\hat{y}_0$ is $f(x_0)$? I think: $E(\hat{y}_0)=E(x_0^T\hat{\beta})=x_0^T\beta=f(x_0)$. So why $E_{\mathcal{T}}(f(x_0)-\hat{y_0})^2=Var_{\mathcal{T}}(\hat{y_0})+Bias^2(\hat{y}_0)$? Isn't it only equals the Var? Why there is also a Bias.

Maybe a silly problem...But I feel so confused. I need your help!thank you!

Answer 1

I think in general the expression theyve written is correct, since the bias is not always $0$. But in this case (you can see on the next line) the bias is $0$.