Question 4: Consider a biased random walk (with positive drift) as follows: 1, with probability p, Yi -1, with probability q = 1 p 0 be two positive numbers. We are interested in finding the probability ha of the random walk reaching -a before reaching b. Hint: From lectures, we know that X = with X = 0 is a martingale that is used to deal with symmetric random walk. Now, for an asymmetric random walk, consider a sequence of transformed random variables X = 1, = and show that this transformed sequence is a martingale and then use Optional Sampling Theorem.