I wish to evaluate the following:
$E[W(t-1)W(t)^2]$
$E[W(t)^3]$
where $t > 1$, $W$ is a standard Brownian motion and we are at $\mathscr{F}_0$ now.
I know that $E[W(t-1)W(t)] = \min{(t-1,t)} = (t-1)$ when $W$ is a standard Brownian motion, but I'm not sure how to solve the above expectations. I could do it easily if I could go $E[W(t-1)W(t)^2]=E[W(t-1)]E[W(t)^2]=0$ (duh); however I can't do this beacuse they're dependent random variables.
Thanks.