Commute Time Between Endpoints of a Path

Consider the path graph $P_n$ with vertices $\{0, 1, \ldots, n-1\}$ and $n-1$ edges (each of unit resistance), where the walk at interior vertices moves left or right with equal probability, and at the endpoints moves to the unique neighbor.

(a) Compute the effective resistance $R_{\mathrm{eff}}(0, n-1)$ between the two endpoints.

(b) Using $C(u,v) = 2m \cdot R_{\mathrm{eff}}(u,v)$, find the commute time between the two endpoints.

(c) Verify for $n = 4$ by computing $h(0 \to 3)$ and $h(3 \to 0)$ directly.