# Compatibility of conditional and marginal independence assumptions

I want to know if two independence assumptions, as illustrated below, would go together or not.

Consider I have 4 variables, A,B,C,D. Can the following two independence assumptions co-exist?

$$A \perp B | C,D$$ and $$(A,C) \perp D$$ ?

• In term of pdf (probability density function) what do that two things mean? – user158565 Oct 20 '18 at 20:27
• how about a <- c -> b <- d – user20650 Oct 20 '18 at 23:30