Solution
= Solution
The graph has six edges, and $A$ has degree one. Hence $\pi_A=1/12$. Kac's return-time formula gives
$$
\boxed{\mathbb E_A T_A^+=\frac1{\pi_A}=12.}
$$
= Solution
The graph has six edges, and $A$ has degree one. Hence $\pi_A=1/12$. Kac's return-time formula gives
$$
\boxed{\mathbb E_A T_A^+=\frac1{\pi_A}=12.}
$$