I'm reading a book on synthetic aperture radar and it is said that:
The term $\sigma^{\circ}$ is the averaged radar cross section per unit area, also called the scattering coefficient or
sigma-naughtand represents the ratio of the statistically averaged scattered power density to the average incident power density over the surface of the sphere of radius r with
$$\sigma^{\circ}=\frac{\langle\sigma\rangle}{A_0}=\frac{4\pi r^2}{A_0}\frac{\langle|\vec E_S|^2\rangle}{|\vec E_I|^2}$$ I mean what statistical or mathematical concept does the $\langle\;\rangle$ show here?
From statistics which I have studied in the first year of university I'm familiar with these concepts:
arithmetic mean for the sample: $$\overline x=\frac{\sum_{i=1}^n x_i}{n}$$ arithmetic mean for the society:$$\mu=\frac{\sum_{i=1}^n x_i}{N}$$ Expected value for a discrete random variable:$$E(X)=\sum_{\forall x_i}x_iP_X(x_i)$$ Expected value for a continuous random variable: $$E(X)=\int_{-\infty}^{+\infty}xf_X(x)dx$$ $f_X(x)$ and $P_X(x_i)$ are probability density functions.
But I don't know which of them is called average and which one is called statistical average?
what's the purpose of average and statistical average?
what's the mathematical formula for each of them?