I'm supposed to compute
$E\left(W_6 | W_2 , W_4\right)$ knowing that $W$ is a standard Brownian motion.
I found $W_2$ but it's weird... Any help ?
2026-03-28 20:51:21.1774731081
3 Brownian motion and conditional expectation
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$E(W_6|W_2,W_4)=E(W_6-W_4|W_2,W_4)+E(W_4|W_2,W_4)=E(W_6-W_4)+W_4=0+W_4=W_4$.
For the second inequality I have used independence of $W_6-W_4$ and $(W_2,W_4)$