Introduction
Given that X(t) is a second-order ergodic stationary process, we must estimate the theoretical average.
\(m=E\left\{x\left(t\right)\right\}=\lim\limits_{T \to \infty} \frac {1} {T}=\int_{-\frac{T}{2}}^{+\frac{T}{2}} \mathrm{x(t)}\,\mathrm{d}x=constant\)
From a single T duration realisation of x(t), so be it:
\(\hat{m}=E\left\{x\left(t\right)\right\}=\frac{\mathrm{1} }{T}\int_{\mathrm{0}}^{T}x\left(t\right)dt\) (4)
(4) can be considered a particular achievement of the R.V.:
\(\hat{M}=E\left\{x\left(t\right)\right\}=\frac{\mathrm{1} }{T}\int_{\mathrm{0}}^{T}x\left(t\right)dt\) (5)