What is $C=\sigma^2/n+\mu^2$

Question

I frequently see the notation $C$ in probability theory:

$$C=\sigma^2/n+\mu^2$$

What is the meaning of $C$?

Answer 1

It is the second moment of the sample mean $\overline{X} = \frac{1}{n} \sum_{i=1}^n X_i$:

$$\mathrm{E}(\overline{X}^2) = \mathrm{E}(\overline{X})^2 + \mathrm{Var}(\overline{X}) = \mu^2 + \frac{\sigma^2}{n}$$