random walk

a. Consider a random walk S = >. X, , where So = 0, and iid random variables X, are distributed as follows: P[X = 1] = 2/3 and P[X = 2] = 1/3. (i) Assume the walk terminates whenever the walker either steps on po- sition k > 0, or oversteps it for the first time. Use the method of first-step decomposition to calculate the probability that the walker does step on k. [10 marks]