Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 221 / 1 / ii / Solution

The directed acyclic graph factorization isThe graph gives $U\perp X_1$ and $U\perp X_3\mid (X_1,X_2)$. Therefore Bayes theorem givesConsequentlywhich contains no $x_1$. This observed equality is a Verma constraint: it is implied by the latent-variable causal graph even though it is not a conditional independence.