For a simple random walk with absorbing barriers at 0 and N. Let W be the event that the particle is absorbed at 0 rather than N., and let . Show that if the particle starts at k where 0 < k < N, the conditional probability that the first step is rightwards, given W, equals . Deduce that the mean duration of the walk, conditional on W, satisfies the equation
I get:
For the next part
however i get stuck here, i wonder if i have the right idea