1. Consider n independent ?ips of a coin having probability p of landing heads. Say a changeover occurs whenever an outcome differs from the one preceding it. For instance, if the results of the ?ips are H H T H T H H T, then there are a total of ?ve changeovers. If p = 1/2, what is the probability there are k changeovers?
2. Let X be a Poisson random variable with parameter λ. Show that P{X = i} increases monotonically and then decreases monotonically as i increases, reaching its maxi- mum when i is the largest integer not exceeding λ.