Exercise 32.2. Hurricanes. On the average, hurricane of category 4 or stronger (

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 uricane that is category 4 or stronger.

Explanation / Answer

Ans:

h)cdf:

P(X<=x)=1-e-x/6

P(X>=3)=e-3/6=e-0.5=0.6065

i)P(5<=X<=10)=P(X<=10)-P(X<=5)=e-5/6-e-10/6

=e-0.833-e-1.667=0.4346-0.1889=0.2457

j)As,exponential distribution is memoryless,so,We have to find probability that there are no hurricanes in next 7 years.

P(X>7)=e-7/6=e-1.167=0.3114

k)

P(X<=x)=0.75

1-e-x/6=0.75

e-x/6=1-0.75=0.25

x/6=-ln(0.25)=1.3863

x=8.32 years

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