On the average, a category 4 (on the Stafford/Simpson scale) or stronger hurricane 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, (www.aoml.noaa.gov/ hrd/Landsea/deadly/index.html) An insurance agency is considering whether they 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 3 hurricanes that are category 4 or stronger.
a. Why is this Gamma scenario?
b. What does X represent in this scenario?
c. What are the parameters?
d. What is the expected length of time (in years) between now and when the third hurricane that is category 4 or stronger will come?
e. What is the variance in this length of time?
f. What is the probability density function for the length of time before the third hurricane that is category 4 or stronger will come? Write your answer in function form and show a graph.
g. What is the CDF for the length of time before the third hurricane that is category 4 or stronger? Write your answer in function form and show a graph.
h. What is the probability that the third hurricane that is category 4 or .stronger will arrive in the next 10 years?