Regarding Brownian Motion formula below, how does $E[W(s)W(t)]$ turn into $$E\left[W(s)\big(W(t)−W(s)\big)+W(s)^2\right]\;??$$
I have asked a question using the formula below, but this and that are totally different questions. Thanks for all the help!!
Assuming $t>s$,
$$\begin{align*} E[W(s)W(t)]&=E\left[W(s)\big(W(t)−W(s)\big)+W(s)^2\right]\\ &=E[W(s)]E[W(t)−W(s)]+E\left[W(s)^2\right]\\ &=0+s\\ &=\min(s,t)\;. \end{align*}$$