1. A country is subjected to natural hazards such as floods, earthquakes, and tornadoes. Suppose earthquakes occur according to a Poisson process with a mean rate of one in 10 years tornado occurrences are also Poisson distributed with a mean rate of 0.3 per year. There can be either one or no flood each year; hence the occurrence of a flood each year follows a Bernoulli sequence, and the mean return period (i.e. interval between repeat events) of floods is five years. Assume floods, earthquakes, and tornadoes can occur independently. a. If no hazards occur during a given year, it is referred to as a good year. What is the probability of a good year? b. What is the probability that two of the next five years will be good years? C. What is the probability of only one incidence of natural hazard in a given year? 2. An oil drilling company ventures into various locations, and its success or failure is independent from one location to another. Suppose the probability of a success at any specific location is 0.25. a. What is the probability that a driller drills 10 locations and finds 1 success? b. The driller feels that he will go bankrupt if he drills 10 times before the first success occurs. What are the chances that the driller will face bankruptcy?
A country is subjected to natural hazards such as floods, earthquakes, and tornadoes.
Suppose earthquakes occur according to a Poisson process with a mean rate of one in 10
years tornado occurrences are also Poisson distributed with a mean rate of 0.3 per year.
There can be either one or no flood each year; hence the occurrence of a flood each year
follows a Bernoulli sequence, and the mean return period (i.e. interval between repeat
events) of floods is five years. Assume floods, earthquakes, and tornadoes can occur
independently.
a. If no hazards occur during a given year, it is referred to as a good year. What is the
probability of a good year?
b. What is the probability that two of the next five years will be good years?
c. What is the probability of only one incidence of natural hazard in a given year?
2. An oil drilling company ventures into various locations, and its success or failure is
independent from one location to another. Suppose the probability of a success at any
specific location is 0.25.
a. What is the probability that a driller drills 10 locations and finds 1 success?
b. The driller feels that he will go bankrupt if he drills 10 times before the first success
occurs. What are the chances that the driller will face bankruptcy?
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