\operatorname{E}[M_t] = \int_0^\infty m f_{M_t}(m)\,dm = \int_0^\infty m \sqrt{\frac{2}{\pi t}}e^{-\frac{m^2}{2t}}\,dm = \sqrt{\frac{2t}{\pi}} .
The process V_t = W_1 - W_{1-t} for 0 ≤ t ≤ 1 is distributed like Wt for 0 ≤ t ≤ 1.