Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 221 / 3 / b / Solution

A backdoor path from $A$ to $Y$ is a path whose first edge has an arrowhead at $A$. The set $X_I$ satisfies the backdoor criterion when it contains no descendant of $A$ and blocks every backdoor path from $A$ to $Y$. Under this criterion, consistency, and positivity,so adjustment for $X_I$ identifies the intervention mean.