Question

The number of hurricanes (Y) in a season follows a Poisson distribution with a mean of 3. The damage (X) done by a hurricane during a given season follows an exponential distribution with mean 2Y.

What is the variance of the yearly damage?

Answer #1

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 5.6 per year.
a. Find the probability that, in a year, there will be 3
hurricanes.
b. In a 35-year period, how many years are expected to have 3
hurricanes?
c. How does the result from part (b) compare to a recent period
of 35 years in which 3 years had 3 hurricanes? Does the Poisson
distribution work well here?

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 5.2 per year. a. Find the
probability that, in a year, there will be 4 hurricanes. b. In a 45
-year period, how many years are expected to have 4 hurricanes? c.
How does the result from part (b) compare to a recent period of 45
years in which 7 years had 4 hurricanes? Does the Poisson
distribution work well here? a....

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 7.1 per year.
a. Find the probability that, in a year, there will be 5
hurricanes.
b. In a 45 year period, how many years are expected to have 5
hurricanes?
c. How does the result from part (b) compare to a recent period
of 45 years in which 5 years had 5 hurricanes? Does the Poisson
distribution work well here?

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 5.2 per year.
a. Find the probability that, in a year, there will be 4
hurricanes.
b. In a 35-year period, how many years are expected to have 4
hurricanes?
c. How does the result from part (b) compare to a recent period
of 35 years in which 5 years had 4 hurricanes? Does the Poisson
distribution work well here?

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 6.9 per year. a. Find the
probability that, in a year, there will be 4 hurricanes. b. In a
55-year period, how many years are expected to have 4
hurricanes? c. How does the result from part (b) compare to a
recent period of 55 years in which 5 years had 4 hurricnes? Does
the Poisson distribution work well here? (Round to...

Find the indicated probabilities using the geometric
distribution, the Poisson distribution, or the binomial
distribution. Then determine if the events are unusual. If
convenient, use the appropriate probability table or technology to
find the probabilities. A major hurricane is a hurricane with wind
speeds of 111 miles per hour or greater. During the last century,
the mean number of major hurricanes to strike a certain country's
mainland per year was about 0.6. Find the probability that in a
given year...

Find the indicated probabilities using the geometric
distribution, the Poisson distribution, or the binomial
distribution. Then determine if the events are unusual. If
convenient, use the appropriate probability table or technology to
find the probabilities. A major hurricane is a hurricane with wind
speeds of 111 miles per hour or greater. During the last century,
the mean number of major hurricanes to strike a certain country's
mainland per year was about 0.48. Find the probability that in a
given year...

The number of times a geyser erupts in one day follows a Poisson
distribution with mean 2.5. On a randomly selected day:
(a) what is the probability that there are no eruptions? (b)
what is the probability of at least 3 eruptions?

Over the past 15 years, the numbers of hurricanes per year to
cause damage in a particular city were 4, 2, 1, 3, 0, 2, 1, 3, 5,
2, 3, 1, 1, 2, and 0.
What is the probability of not having hurricane damage in any 1
year?
What are the average and variance of the number of hurricanes in
1 year?

the daily number of visitors to a national park follows a
Poisson distribution with mean 900.
calculate the 80th percentile of the number of visitors in a
day.

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