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

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

Any help will be great.

Thank you.