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$\textbf{z}=(z_1, z_2)$ categorical vector   $\textbf{x}=(x_1,...,x_N)$ vector of observations, where $x_i $x_i|z_j=1  \sim N(\mu_{z_j}, \sigma^2_{z_j})$, $j = 1,2$ N(\mu_{1}, \sigma^2_{1})$, $x_i|z_j=2 \sim N(\mu_{2}, \sigma^2_{2})$  Expactation-Maximization method consists of E-step and M-step.