The number of earthquakes that occur per week in Californiafollows a Poisson distribution with a
mean of 1.5.
(a) What is the probability that an earthquake occurs within thefirst week? Show by hand and
provide the appropriate R code.
(b) What is the expected amount of time until an earthquakeoccurs?
(c) What is the standard deviation of the amount of time until twoearthquakes occur?
(d) What is the probability that it takes more than a month toobserve 4 earthquakes? Show by hand
(you may simply leave it as an integral) and provide theappropriate R code.
(e) What is the median amount of time it takes for 5 earthquakes tooccur? Show by hand (you may
simply leave it as an integral, but be sure to explain how to findthe median) and provide the
appropriate R code.
