Could you please let me know the steps to follow to get to the solution?

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    $\begingroup$ What have you tried? You are supposed to show your own work so we can help you instead of just doing your homework. $\endgroup$ – Forgottenscience Nov 22 '18 at 12:36

I will have a crack at a) i) for you, assuming $E[W_1] = E[W_2]=0$:

$$ \begin{equation}\begin{split} E[B_1 W_2] & = E[\alpha W_1 W_2 + \sqrt{1-\alpha^2} W_2 W_2] \\ & = \alpha E[W_1 W_2] + \sqrt{1-\alpha^2}E[W_2^2] \quad \text{(inearity of expectation)}\\ & = \alpha E[W_1] E[W_2] + \sqrt{1-\alpha^2}E[W_2^2] \quad \text{(independence)}\\ & = \sqrt{1-\alpha^2} Var(W_2) \quad \text{(definition of variance)} \end{split}\end{equation}$$

Perhaps this helps you with ii)

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