EM parameter estimation for conditional Gaussians
When $X_1$ is unobserved, at iteration $k=1$ of EM, the posterior mean value (when $X_2=3$) is $5.18$ by using an inference algorithm, i.e. Junction tree/kalman filter. 
Then the sufficient statistics for $X_1$ is: 

$s_1=\Sigma_{i=1}^nx_{i1}=9+4+5.18$ and $s_{11}=\Sigma_{i=1}^nx_{i1}^2=9^2+4^2+(5.18^2+\sigma_{11.2})$

where $\sigma_{11.2}$ is the posterior conditional variance of $X_1$ given $X_2$, when $X_1$ is unobserved. 

$s_2=\Sigma_{i=1}^nx_{i2}$ and $s_{22}=\Sigma_{i=1}^nx_{i2}^2$. When $X_2$ is unobserved a term $\sigma_{22.1}$ is also added to $x_{i2}^2$. 

So parameters $\mu_{X_1}$ and $\sigma_{X_1}$ are obtained. Similarly, posterior mean of unobserved $X_2$ is also obtained by using i.e. Junction tree inference.

The sufficient statistics for $s_{12}=\Sigma_{i=1}^nx_{i1}x_{i2}$, and $s_{21}=\Sigma_{i=1}^nx_{i2}x_{i1}$.

Mean vector is then: $\mu^{(k)}=(s_1/n, s_2/n)$.

Covariance matrix is: $\Sigma^{(k)}=$$\left( \begin{matrix}
   \Sigma _{11} &amp; \Sigma _{12}  \\
   \Sigma _{21} &amp; \Sigma _{22}  \\
\end{matrix} \right)$$=$$\left( \begin{matrix}
   s_{11}/n-(s_1/n)^2 &amp; s_{21}/n-(s_2/n)(s_1/n)  \\
   s_{12}/n-(s_1/n)(s_2/n) &amp; s_{22}/n-(s_2/n)^2  \\
\end{matrix} \right)$$
 $

Other parameters in the question are obtained. Conditional mean and conditional variance of $X_2|X_1$ is calculated by the formula in the reference of the question.