I want to have a mixture model like $\lambda \cdot P(s'|s, a) + (1- \lambda) \cdot P'(s'|s)$ where $P$ and $P'$ are conditional distributions and $\lambda \in [0,1]$ is a weight. I have two questions about the model.
- Is it true that the entire mixture model is still dependent on $a$ because its component $P$ is conditioned on $a$? Thus, can I write the mixture model as $P''(s'|s,a)$?
- This is a general question about any mixture model: should I interpret a mixture model as 1) first sampling a distribution based on given weights and then 2) sampling from the chosen distribution? Or, is it okay to interpret the model as we are just sampling once from the mixture model? I just started learning statistics, so I am not sure if this kind of interpretation even matters.