= Solution
The three independent <sample means> satisfy $\overline Y_i\sim\mathcal N(\mu_i,v_i)$. A linear transformation of their joint <multivariate normal distribution> is again normal. The two treatment contrasts have <covariance>
$$
\operatorname{Cov}(\overline Y_1-\overline Y_0,\overline Y_2-\overline Y_0)=\operatorname{Var}(\overline Y_0)=v_0.
$$
Writing $m_i=\delta_i/s_i$ and $\rho=v_0/(s_1s_2)$, \b[their joint distribution] is
$$
\boxed{\begin{pmatrix}W_1\\W_2\end{pmatrix}\sim\mathcal N_2\left(\begin{pmatrix}m_1\\m_2\end{pmatrix},\begin{pmatrix}1&\rho\\\rho&1\end{pmatrix}\right).}
$$
The positive <correlation coefficient> arises from the shared control arm. Under positive variances, $0<\rho<1$.
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