$$Y_i \sim N_K \left( X_i \beta , \Sigma\right), i = 1, \ldots, n$$
$$\begin{align}\beta^{(t + 1)} = & \left( \sum_{i=1}^n X_i^T (\Sigma^{(t)})^{-1}X_i\right)^{-1} \\ & \cdot \left( \sum_{i=1}^n X_i^T (\Sigma^{(t)})^{-1}Y_i\right)\end{align}$$
$$\Sigma^{t+1} = \frac{1}{n} \sum_{i=1}^n (Y_i - X_i \beta^{(t+1)}) (Y_i - X_i \beta^{(t+1)})^T$$
$$\begin{align} l( \beta^{(t+1)}, \Sigma^{(t)} \given Y) & \geq l( \beta^{(t)}, \Sigma^{(t)} \given Y) \\ l( \beta^{(t+1)}, \Sigma^{(t+1)} \given Y) & \geq l( \beta^{(t+1)}, \Sigma^{(t)} \given Y)\end{align}$$
$$\begin{align}&l(\mu, \Sigma \given Y_{\rr{obs}}) = const - \frac{1}{2} \sum_{i=1}^n log |\Sigma_{\rr{obs}, i}| \\ & - \frac{1}{2} \sum_{i=1}^n (y_{\rr{obs}, i} -\mu_{\rr{obs}, i})^T \Sigma^{-1}_{\rr{obs}, i} (y_{\rr{obs}, i} - \mu_{\rr{obs}, i})\end{align}$$
$$\begin{align}S = &\left( \sum_{i=1}^n y_{ij}, \rr{ } j= 1, \ldots K; \right. \\ & \left. \sum_{i=1}^n y_{ij} y_{ik}, \rr{ } j, k = 1, \ldots, K\right)\end{align}$$
$$E \left( \sum_{i=1}^n y_{ij} \given Y_{\rr{obs}}, \theta^{(t)}\right) = \sum_{i=1}^n y_{ij}^{(t)}, \rr{ } j=1, \ldots, K$$
$$\begin{align}E \left( \sum_{i=1}^n y_{ij}y_{ik} \given Y_{\rr{obs}}, \theta^{(t)}\right) = & \sum_{i=1}^n (y_{ij}^{(t)}y_{ik}^{(t)} + c_{jki}^{(t)}), \\ &j,k=1, \ldots, K\end{align}$$
$$y_{ij}^{(t)} = \begin{cases} y_{ij} & y_{ij} \rr{ is observed} \\ E(y_{ij} \given y_{\rr{obs}, i}, \theta^{(t)}) & y_{ij} \rr{ is missing}\end{cases}$$
$$c_{jki}^{(t)} = \begin{cases} 0 & y_{ij} \rr{ or } y_{ik} \rr{ obs} \\ \rr{Cov}(y_{ij}, y_{ik} \given y_{\rr{obs}, i}, \theta^{(t)}) & \rr{otherwise}\end{cases}$$
$$f(x_i \given \theta) \sim \frac{\Gamma(\nu / 2 + 1/2)}{\sqrt{\pi\nu \sigma^2} \Gamma(\nu / 2) \left[1 + \frac{(x_i - \mu)^2}{\nu \sigma^2}\right]^{(\nu + 1) / 2}}$$
$$x_i \given \theta, w_i \mathop{\sim}^{\rr{ind}} N( \mu, \sigma^2/w_i), \rr{ } w_i \given \theta \sim \chi^2_\nu / \nu$$
$$s_0 = \sum_{i=1}^n w_i, \rr{ } s_1 = \sum_{i=1}^n w_i x_i, \rr{ } s_2 = \sum_{i=1}^n w_i x_i^2$$
$$w_i^{(t)} = E(w_i \given x_i, \theta) = \frac{\nu + 1}{\nu + d_i^{(t)^2}}$$
$$\begin{align}\mu^{(t+1)} & = \frac{s_1^{(t)}}{s_0^{(t)}} \\ \hat{\sigma}^{(t+1)^2} & = \frac{1}{n} \sum_{i=1}^n w_i^{(t)} (x_i - \hat{\mu}^{(t+1)})^2 \\ & = \frac{s_2^{(t)} - s_1^{(t)^2} / s_0^{(t)}}{n}\end{align}$$