Suppose I have an observation $Y_t$ that is conditionally dependent on $X_t$. (More specifically, Y is a series of observations emitted by an underlying hidden Markov state sequence X.)
I can describe the distribution of $p(Y_t)$ as
that is to say, the sum of the emission probabilities for all possible hidden states.
My question is, suppose I also have a third variable Z. Can I express $p(Y_t|z)$ as: