Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 215 / 4 / a / Solution

For each fixed output state $y$, the right-shift part has exactly two predecessors, each contributing $1/3$, and the left-shift part also has exactly two predecessors, each contributing $1/6$. Thus every column sum isThe transition matrix is doubly stochastic, so the uniform lawis invariant.