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?
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?
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?
Transcribed Image Text: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?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
