For given $\mu,\sigma$, I would like to get an expression for the expectation of a discretized normal, specifically $E(\lceil N(\mu,\sigma^2)\rceil)$.
I know how to write the infinite sum, but that does not help me analyze the expectation. I'm interested in (i) a closed form expression or (ii) if it's not possible, an approximation. For (ii), I'm in a setting where the std is not large, say $\sigma\leq \mu$.
Thanks!