Suppose we are counting successes in a Poisson process where we expect 12 successes per hour.  How many successes are expected during a 25 minute period?

Suppose we are counting successes in a Poisson process where we expect 15 successes per hour.  What is the probability that we have to wait at most 23 minutes but more than 15 minutes to have five successes?

Suppose we are counting successes in a Poisson process where we expect 1/4 of a  success per minute.  What is the standard deviation in the time we must wait to have the first success? Group of answer choices

Occurrences of landfalling hurricanes during an El Niño event are modeled asa Poisson process in Bove et al. (1998). The authors assert that “During an ElNiño year, the probability of two or more hurricanes making landfall in theUnited States is 28%.” Find the rate of the Poisson process.

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Suppose bird attacks follow a Poisson process and attacks occur at a rate of 4 attacks per week What is the probability of a bird free week (0 bird attacks)? In a period of 16 weeks, what is the probability of exactly 2 bird free weeks? What is the probability that it takes 16 weeks for there to be exactly 3 bird free weeks?

Follow up question: You want to model customers arriving in a shop using this process instead of a Poisson Process. Using a random variable to determine the increments allows us to include a feature which the Poisson Process cannot. Write down this feature in non-mathematical language.

Suppose we are counting successes in a Poisson process where we expect 15 successes per hour.  What is the expected time we must wait to have 20 successes?