Let $$W_t$$ and $$B_t$$ be two independent standard Brownian Motions. For $$\rho \in [0,1]$$ define
$Z_t = {\rho}\, W_t +\sqrt{1-\rho^2}\, B_t$
1. Why is $$Z_t$$ a standard Brownian Motion ?
2. Calculate  the cross-quadratic variations $$[ Z,W]_t$$ and $$[ Z,B]_t$$ .
3. For what values of $$\rho$$ is $$W_t$$ independent of $$Z_t$$ ?