Question: 4. Humanity is on the run through space, being chased by killer robots that attack on average every 33 minutes. Assume the killer robot attacks

4. Humanity is on the run through space, being chased by killer robots that attack on average every 33 minutes. Assume the killer robot attacks occur following a Poisson process. a. What is the distribution of the number of attacks that occur per hour? (3pt) b. No attack has occurred in the last fifteen minutes. What is the probability it will be more than another fifteen minutes until the next attack? (3pt) c. What is the expected number of attacks that will occur over a 12 hour period? (3pt) d. The humans have to perform critical maintenance on their defensive systems. The repairs will take 12 minutes. What is the probability there are one or more attacks in this 12 minute period? (4pt)

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