= Solution
Let $X$ denote the observed data, $Z$ the unobserved data and $\theta$ the model parameters. The <expectation-maximization algorithm> works with the complete-data <log-likelihood> $\ell_c(\theta;X,Z)$. Given $\theta^{(r)}$, its \b[E-step] computes
$$
Q(\theta\mid\theta^{(r)})=E_{\theta^{(r)}}[\ell_c(\theta;X,Z)\mid X],
$$
where the <conditional expectation> uses the old parameter, while $\theta$ remains the argument to maximize. Its \b[M-step] chooses $\theta^{(r+1)}$ maximizing this function over the parameter space. <EM likelihood monotonicity> ensures that an M-step increasing $Q$ cannot decrease the observed-data <log-likelihood>. It does not guarantee a global maximum, so convergence and any parameter constraints must still be checked.
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