I have a Dirac delta function as follows:
$\delta_{\epsilon = y}$ where $\epsilon \sim N(0, \sigma^2)$, and $y \in \mathbb{R}$.
I want to take the expectation of this function, but it appears that it would, by definition, be $\infty * P(\epsilon = y)$, which isn't well defined.
Is that accurate, or am I missing something here.