Question

# Coastal businesses along the Gulf ofMexico from Texas to Florida worry about the threat of hurricanes...

Coastal businesses along the Gulf ofMexico from Texas to Florida worry about the threat of hurricanes during the season from June through October. Businesses become especially nervous when hurricanes enter the Gulf of Mexico. Suppose the arrival of hurricanes during this season is Poisson distributed, with an average of three hurricanes entering the Gulf of Mexico during the five-month season. If a hurricane has just entered the Gulf of Mexico: a. What is the probability that at least one month will pass before the next hurricane enters the Gulf? b. What is the probability that another hurricane will enter the Gulf of Mexico in two weeks or less? c. What is the average amount of time between hurricanes entering the Gulf of Mexico?

The number of hurricanes that enter the Gulf of Mexico in time is a random variable can be modeled by Poisson distribution.

The Poisson PMF is

Here is the Poisson parameter - the average number of events in unit time.

The interarrival times of the hurricanes has Exponential distribution with .
a) The probability that at least one month will pass before the next hurricane enters the Gulf is

b) The probability that another hurricane will enter the Gulf of Mexico in two weeks or less (2 weeks is 1/2 month)

c) The average amount of time between hurricanes entering the Gulf of Mexico is the average value of interarrival times which is

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