details of stochastic Expectation Maximization (EM) algorithm I went into a paper, Online EM Algorithm for Latent Data Models (Olivier Cappé & Eric Moulines, 2009). I got confused by the first equation the authors wrote, the Q function:

Here the authors denoted $X$ to be the latent variable, and $Y$ to be the observed variable. My question is:
Shouldn't $f(X_i; \theta)$ be $f(X_i, Y_i; \theta)$ instead?

If you read a few lines above, this is a model where

The observation $Y$ is then viewed as a deterministic function of $X$
which takes its values in the set $\mathcal Y$

This means that the joint distribution of $(X,Y)$ appearing in the $Q(\cdot;\cdot)$ function is the distribution of $X$.
