(Exponential Distribution, 10 points) Suppose that earthquakes occur in California according to an exponential distribut

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Exponential Distribution 10 Points Suppose That Earthquakes Occur In California According To An Exponential Distribut 1 (158.73 KiB) Viewed 47 times

(Exponential Distribution, 10 points) Suppose that earthquakes occur in California according to an exponential distribution, with an average of 4 earthquakes per year. (a) What is the probability that the first earthquake of 2023 will occur during March? (Hint: 2023 is not a leap year, so January and March have 31 days and February has 28 days, and you should calculate with a time unit of days.) (b) What is the probability that in exactly 4 of the next 10 years, no earthquakes occur? For the following, we will use the Poisson distribution, which is a discrete"counting distribution" related to the exponential. If is the rate (e.g., 4 per month), then the random variable X- Poisson(1) if X is the number of arrivals that show up in a given unit of time. The PDF is e-l1-k Pr(X = k) = k! Unfortunately there is no easy way to calculate the CDF, it is like the binomial, you just have to do sums over the PDF. (c) What is the expected number of months to wait until we have a month with exactly 2 earth- quakes? Use a time unit of months, and for simplicity assume that each month is 1/12th of a year. (d) In the next 50 years, how many years would you expect to see with more than 8 earthquakes?