Consider two assets whose prices \(S_{t}^{(1)}, S_{t}^{(2)}\) at time \(t \in[0, T]\) follow the geometric Brownian dynamics

\[
d S_{t}^{(1)}=\mu S_{t}^{(1)} d t+\sigma_{1} S_{t}^{(1)} d W_{t}^{(1)} \text { and } d S_{t}^{(2)}=\mu S_{t}^{(2)} d t+\sigma_{2} S_{t}^{(2)} d W_{t}^{(2)}
\]

\(t \in[0, T]\), where \(\left(W_{t}^{(1)}ight)_{t \in[0, T]},\left(W_{t}^{(2)}ight)_{t \in[0, T]}\) are two Brownian motions with correlation \(ho \in[-1,1]\), i.e. we have \(\mathbb{E}\left[W_{t}^{(1)} W_{t}^{(2)}ight]=ho t\).

a) Compute \(\mathbb{E}\left[S_{t}^{(i)}ight], t \in[0, T], i=1,2\).

b) Compute \(\operatorname{Var}\left[S_{t}^{(i)}ight], t \in[0, T], i=1,2\).

c) Compute \(\operatorname{Var}\left[S_{t}^{(2)}-S_{t}^{(1)}ight], t \in[0, T]\).