Problem 3. (5 points) One hundred year floods are floods of such a size as to...
Problem 3. (5 points) One hundred year floods are floods of such a size
as to happen only once every hundred years on average. Assume the number of
such floods occurring in a given time period has a Poisson distribution. Find the
probability that 2 or more hundred year floods will occur in a given 150 year
time period.
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Problem 3. (5 points) One hundred year floods are floods of such
a size
as to...
4. A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Supposé earthquakes...
4. A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Supposé earthquakes occur according to a Poisson process with a mean rate of 1 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 returm period of floods is 5 years. Assume floods, earthquakes, and...
please to find the question in the image. thank you A system (e.g. a dam or...
please to find the question in
the image. thank you
A system (e.g. a dam or a dike) is said to be designed for the N-year flood if it has a capacity which will be exceeded by a flood equal or greater that the N-year flood. The magnitude of the N-year flood. The magnitude of the N-year flood is that which is exceeded with probability 1/N in any given year. Assume that successive annual floods are independent. a)- What is...
An article suggests that a Poisson process can be used to represent the occurrence of structural...
An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.5 year. For every single part, clearly define the random variable of interest using the context of this problem. (Hint: We are given that the mean time between occurrences of loads is 0.5 year. It is not the λ value to be used in Poisson process since it is the mean time...
2. (Discrete distributions, 20 points, 20/3 pts each). From a recent statistical analysis for the last...
2. (Discrete distributions, 20 points, 20/3 pts each). From a recent statistical analysis for the last five years, on an average there are 4.1 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X-Poisson() approximately, where the intensity 2. = 4.1 accidents (average number of accidents per month). Find the probability that there will be 4 or more air accidents (1) in a...
Suppose traffic accidents at a road intersection occur once every 7 days. It can be assumed...
Suppose traffic accidents at a road intersection occur once every 7 days. It can be assumed there is no more than 1 accident occurring at this intersection simultaneously, and at this intersection accidents can occur at any time. Also, an accident is not due to other accidents. (What type of distribution is this i.e. Gaussian, Poisson, etc.?) What is the probability that there are 3 accidents during the next 15 days at the intersection? Calculate by hand. What is the...
4. At a local hospital, babies are born at an average rate of four births per...
4. At a local hospital, babies are born at an average rate of four births per night (consider "night" to be an 8 hour period from 10pm to 6am). Assume that the time that elapsed from one birth to the next has the exponential distribution. Take note that we are concerned only with the rate at which babies are born, and we are ignoring the time spent in labor. We must also assume that the times spent between births are...
7, If the number of event occurrences is Poisson distributed, successive occurrences is exponentially distributed. In...
7, If the number of event occurrences is Poisson distributed, successive occurrences is exponentially distributed. In certain locations in Texas, sudden heavy rainfall may produce sudden floods, called flash floods, because of the land surface geometry and other geographical factors. If a flood (event) occurs in any one day, we may the day a "flood day.' The flood days average 10 per year based on data over many years past i. Find the probability that 8 flood days will occur...
PLEASE DO ASAP Alt Ctri (20 points) On one particular road in the city, th follows...
PLEASE DO ASAP
Alt Ctri (20 points) On one particular road in the city, th follows a Poisson distribution with ?-3, and the follows an exponential distribution with 0-8 hours. e number of traffic accidents time in between traffic accidents 5. A In a given day, what is the probablity that there are more than 5 traffic accidents in the city? B. What is the probability that another accident occurs within 5 hours since last C. one in that day?...
3. From 2000-2019 there were a total of 3071 earthquakes worldwide with a magnitude of 6...
3. From 2000-2019 there were a total of 3071 earthquakes worldwide with a magnitude of 6 or greater, or an average of about 0.42 such earthquakes per day.* Assume that moving forward the total number of such earthquakes to occur over any time period follows a Poisson distribution with an average of 0.42 earthquakes per day. For the remainder of this question, "earthquake" will mean an earthquake with a magnitude of 6 or greater. Define a new random variable as...
Problem 7: [8 points] The length of time to failure (in hundred of hours) for a...
Problem 7: [8 points] The length of time to failure (in hundred of hours) for a transistor is a random variable Y with c.d.f. given by F(y) {: 1 - exp{-yº}, if y20, 0, elsewhere. (a) Find the p.d.f f(y) of Y and show that it is indeed a valid p.d.f [2] (b) Find the 30th percentile of Y and interpret it [2]. (c) Find E(Y) and V(Y) [2] (d) Find the probability that the transistor operates for at least...
4. A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Supposé earthquakes occur according to a Poisson process with a mean rate of 1 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 returm period of floods is 5 years. Assume floods, earthquakes, and...
please to find the question in
the image. thank you
A system (e.g. a dam or a dike) is said to be designed for the N-year flood if it has a capacity which will be exceeded by a flood equal or greater that the N-year flood. The magnitude of the N-year flood. The magnitude of the N-year flood is that which is exceeded with probability 1/N in any given year. Assume that successive annual floods are independent. a)- What is...
2. (Discrete distributions, 20 points, 20/3 pts each). From a recent statistical analysis for the last five years, on an average there are 4.1 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X-Poisson() approximately, where the intensity 2. = 4.1 accidents (average number of accidents per month). Find the probability that there will be 4 or more air accidents (1) in a...
4. At a local hospital, babies are born at an average rate of four births per night (consider "night" to be an 8 hour period from 10pm to 6am). Assume that the time that elapsed from one birth to the next has the exponential distribution. Take note that we are concerned only with the rate at which babies are born, and we are ignoring the time spent in labor. We must also assume that the times spent between births are...
7, If the number of event occurrences is Poisson distributed, successive occurrences is exponentially distributed. In certain locations in Texas, sudden heavy rainfall may produce sudden floods, called flash floods, because of the land surface geometry and other geographical factors. If a flood (event) occurs in any one day, we may the day a "flood day.' The flood days average 10 per year based on data over many years past i. Find the probability that 8 flood days will occur...
PLEASE DO ASAP
Alt Ctri (20 points) On one particular road in the city, th follows a Poisson distribution with ?-3, and the follows an exponential distribution with 0-8 hours. e number of traffic accidents time in between traffic accidents 5. A In a given day, what is the probablity that there are more than 5 traffic accidents in the city? B. What is the probability that another accident occurs within 5 hours since last C. one in that day?...
3. From 2000-2019 there were a total of 3071 earthquakes worldwide with a magnitude of 6 or greater, or an average of about 0.42 such earthquakes per day.* Assume that moving forward the total number of such earthquakes to occur over any time period follows a Poisson distribution with an average of 0.42 earthquakes per day. For the remainder of this question, "earthquake" will mean an earthquake with a magnitude of 6 or greater. Define a new random variable as...
Problem 7: [8 points] The length of time to failure (in hundred of hours) for a transistor is a random variable Y with c.d.f. given by F(y) {: 1 - exp{-yº}, if y20, 0, elsewhere. (a) Find the p.d.f f(y) of Y and show that it is indeed a valid p.d.f [2] (b) Find the 30th percentile of Y and interpret it [2]. (c) Find E(Y) and V(Y) [2] (d) Find the probability that the transistor operates for at least...
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