## More Brownian motion

OK guys here's another one for you....

Let ${B}(t)$ and ${W}(t)$ be two independent Brownian motions. Show that ${X}(t)=({B}(t)+{W}(t))/\sqrt{2}$ is also a Brownian motion. Find correlation between ${B}(t)$ and ${X}(t)$.

Any help will be great.

Thank you.