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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.
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Using your simulation results calculate an estimate of the probability that the sum of the dice is 10 and the player is dealt three cards that can be put in sequence.
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