The number of earthquakes that occur per week in California follows a Poisson distribution with a mean of 1.5. (a) What is the probability that an earthquake occurs within the first week? Show by hand and provide the appropriate R code. (b) What is the expected amount of time until an earthquake occurs? (c) What is the standard deviation of the amount of time until two earthquakes occur?
The number of earthquakes that occur per week in California follows a Poisson distribution with a
mean of 1.5.
(a) What is the probability that an earthquake occurs within the first week? Show by hand and
provide the appropriate R code.
(b) What is the expected amount of time until an earthquake occurs?
(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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