Past exam of the mathematics course of the University of Cambridge / 2014 / ib / Paper 4 / 9H / b / i / Solution

The authoritative definition here is $Y_n=|X_n|$. On the conditioning event, $X_{n-1}=0$. Since $p_{0,1}=0$, the additional condition $Y_n=1$ then forces $X_n=-1$. The Markov property therefore givesAs usual, this conditional probability is asserted when the conditioning event has positive probability.