\begin{eqnarray*}
p(Y|X)=
\prod_{n\in{\cal T}}
\prod_{j\in{\cal J}}
\frac{1}{\sqrt{2\pi\sigma_j^2}}
\exp\left[-\frac{(x_{j,\,n} - y_{j,\,n})^2}{2\sigma_j^2}\right]
\end{eqnarray*}