Exercise 32.2. Hurricanes. On the average, hurricane of category 4 or stronger (
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Question
Exercise 32.2. Hurricanes. On the average, hurricane of category 4 or stronger (on the Stafford/Simpson scale) strikes the United States once every 6 years. A hurricane of this strength has winds of at least 131 miles per hour and can cause extreme damage. (http://www.aoml.noaa.gov/hrd/Landsea/ deadly/index.html) An insurance agency is considering whether it might want to stop insuring oceanfront homes and wants to assess the risk involved. The president of the company wants to know how long (in years) before the next hurricane that is category 4 or stronger a. Why is this an Exponential scenario? b. What does X represent in this scenario? c. What is the parameter? d. What is the expected length of time (in years) between now and when the next hurricane that is category 4 or stronger? e. What is the variance in this length of time? f. What is the probability density function for the length of time before the next hurricane that is category 4 or stronger? Write your answer in function form and show a graph. g. What is the CDF for the length of time before the next hurricane that is h. What is the probability that there will not be any hurricane that is i. What is the probability that there wi be a hurricane that is category 4 j. Given that there are no hurricanes that are category 4 or stronger during category 4 or stronger? Write your answer in function form and show a graph. category 4 or stronger, during the next 3 years? or stronger, during the period that is between 5 to 10 years from now? the next 3 years, what is the probability that there will not be any during the next 10 years? k. How long a waiting time do we need, if we want to be 75% sure that there is a hurricane that is category 4 or stronger during the waiting time?Explanation / Answer
a. Natural disasters are rare events and can be modelled by Poisson distribution. Also we know that the waiting time for an event which follows Poisson distribution can be modelled by using the exponential distribution. Hence, this is an Exponential scenario.
B. X is the waiting time in years before the next hurricane that is category 4 or stronger will occur.
C. The parameter lambda = 1/6 per year
D. Expected length of time = 1/lambda = 6 years
E. Variance = 1/lambda^2 = 36 year^2
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