Let \(w \in \mathcal{C}_{(0)}[0,1]\). Find the densities of the following bi-variate random variables:

a) \(\left(\int_{1 / 2}^{t} s^{2} d w(s), w(1 / 2)ight)\) for \(1 / 2 \leqslant t \leqslant 1\);

b) \(\left(\int_{1 / 2}^{t} s^{2} d w(s), w(u+1 / 2)ight)\) for \(0 \leqslant u \leqslant t / 2,1 / 2 \leqslant t \leqslant 1\);

c) \(\left(\int_{1 / 2}^{t} s^{2} d w(s), \int_{1 / 2}^{t} s d w(s)ight)\) for \(1 / 2 \leqslant t \leqslant 1\);

d) \(\left(\int_{1 / 2}^{1} e^{s} d w(s), w(1)-w(1 / 2)ight)\).