I have just begun learning about random variables, and I am already confused for very basic intuitions based on continuous RVs. For my best understanding, I think if I can convert the discrete RVs scenarios to continuous one then it would be much easier for me to make good intuitions. Alright, here are PMFs scenarios that I'd like to convert in terms of PDFs.
My main doubts are:-
How to multiply two PDFs? Like if two conditions must be satisfied for a single continuous RV, and each condition has its own PDF. So how can I write a new PDF that satisfies both the conditions? (If they were PMF then we could have computed the probability for "AND" situation and could have simply multiplied the PMFs as usual)
How to add two PDFs? Like if 2 PDFs are given and for simplicity lets say both belong to mutually exclusive events, so how can I write a new PDF such that if a continuous RV is sampled from it, then it would only exist either in 1st or 2nd PDF. (For a discrete RV, we could have simply related the whole situation in terms of a Venn diagram and could have computed the probability for "OR" situation, that is simply the addition of all PMFs.)
Edit
I'm actually trying to understand the addition of two pdf in this expression:
Which is used in this research paper.
Here, both $p_{data}(x)$ and $p_{g}(x)$ represents pdfs. So what does their addition signify?