Question: Consider a simple random walk on the integer points in which at each step a particle moves one step in the positive direction with probability

Consider a simple random walk on the integer points in which at each step a particle moves one step in the positive direction with probability p, one step in the negative direction with probability p, and remains in the same place with probability q = 1 - 2p (0 Suppose that, instead of starting with a single individual, the initial population size Zo is a random variable that is Poisson distributed with mean A. Show that, in this case, the extinction probability is given, for p>, by exp{(1 - 2p)/p2}.

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