Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 221 / 1 / a / Solution

In a standardized linear structural equation model, attach to every directed edge its path coefficient. Wright path tracing rule says that a covariance is the sum, over admissible unblocked paths between the two variables, of the product of the coefficients along each path; an admissible path does not pass through a collider and does not enter and later leave the same variable in a way that reverses direction twice. The total causal effect of $X$ on $Y$ is the sum of the products of edge coefficients over all directed paths from $X$ to $Y$.