Consider an asymmetric random walk that takes a step to the right with probability p and a step to the left with probability q = 1 − p. Assume that there are two absorbing barriers, a and b, and that...

Consider an asymmetric random walk that takes a step to the right with probability p and a step to the left with probability q = 1 − p. Assume that there are two absorbing barriers, a and b, and that the walk starts at the point k, where b

a. What is the probability that the walk stops at b?

b. What is the mean number of steps until the walk stops?