The number of earthquakes that occur per week in California follows a Poisson distribution with a mean of 1.5. (c) What is the standard deviation of the amount of time until two earthquakes occur? (d) What is the probability that it takes more than a month to observe 4 earthquakes? Show by hand (you may simply leave it as an integral) and provide the appropriate R code. (e) What is the median amount of time it takes for 5 earthquakes to occur? Show by hand (you may simply leave it as an integral, but be sure to explain how to find the median) and provide the appropriate R code.

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The number of earthquakes that occur per week in California follows a Poisson distribution with a
mean of 1.5.

(c) What is the standard deviation of the amount of time until two earthquakes occur?
(d) What is the probability that it takes more than a month to observe 4 earthquakes? Show by hand
(you may simply leave it as an integral) and provide the appropriate R code.
(e) What is the median amount of time it takes for 5 earthquakes to occur? Show by hand (you may
simply leave it as an integral, but be sure to explain how to find the median) and provide the
appropriate R code.

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