Estimation Bias
The bias is equal to:
\(b\left(\hat{M}\right)=E\left\{\hat{M}-m\right\}=E\left\{\hat{M}\right\}-m=\mathrm{0}\) (6)
Since;
\(E\left(\hat{M}\right)=E\left\{\frac{\mathrm{1}}{T}\int_{\mathrm{0}}^{T}x\left(t\right)dt\right\}=\frac{\mathrm{1} }{T}\int_{\mathrm{0}}^{T}E\left\{x\left(t\right)\right\}dt=\frac{\mathrm{1} }{T}\int_{\mathrm{0}}^{T}{mdt=m}\) (7)
is therefore an unbiased estimator.