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(1 point) Consider a system with one component that is subject to failure, and suppose that...
2 (20 polats) A lighting system is comprised of two lightbulbs work indepeedently. Manufacturer fested failure...
2 (20 polats) A lighting system is comprised of two lightbulbs work indepeedently. Manufacturer fested failure of these components and this failure is know n to oceur randomly with rate (.) of 0.5 per year (a) Define the lifetime random variable and its pdf function. What is the expected lifetime? What is the 80% (i.e., top 20%) lifetime years? (b) What is the probability that both lightbulbs are still functioning after 2 years? (Hint: calculate probability of one component functioning...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently....
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
4. Suppose a random number generator generates 20 numbers per second, where each number is drawn...
4. Suppose a random number generator generates 20 numbers per second, where each number is drawn uniformly from the interval 9,10), independently of all other numbers. We are interested in the event that one of the drawn numbers is very close to Usain Bolt's 100m sprint world record, that is, that this number belongs to the interval (9.575, 9.585). (a) Suppose that the random number generator runs for 10 seconds. Use the Poisson approximation to estimate the probability that it...
Suppose we are analyzing data from the exponential distribution, which has density function f (y) =...
Suppose we are analyzing data from the exponential distribution, which has density function f (y) = ò exp (-5y) for y > 0, depending on a single parameter δ > 0, The exponential distribution arises in reliability theory as the waiting time until failure of a system that is subject to a constant risk of failure δ. (a) Using a computer: plot f(y; δ) as a function of y when δ-1. What is the area under this curve, and why?...
(1 point) Suppose that you randomly draw one card from a standard deck of 52 cards....
(1 point) Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace the card, and draw another card. You repeat this process until you have drawn 15 cards in all. What is the probability of drawing at least 5 diamonds? For the experiment above, let X denote the number of diamonds that are drawn. For this random variable, find its expected value and standard deviation E(X)=( o=
(1 point) After 8:00pm on any Thursday, the amount of time a person spends waiting in...
(1 point) After 8:00pm on any Thursday, the amount of time a person spends waiting in line to get into a well- known pub is a random variable represented by X. Suppose we can model the behavior of X with the Exponential probability distribution with a mean of waiting time of 45 minutes. (a) Provide the value of the standard deviation of this distribution. Enter your answer to two decimals. ox= 45 II minutes (b) Suppose you are in line...
1. Suppose that random variables X and Y are independent and have the following properties: E(X)...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
Data For Tasks 1-8, consider the following data: 7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5,...
Data For Tasks 1-8, consider the following data: 7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5, 13.0, 3.2, -1.1, 7.0, 0.5, 3.9, 2.1, 4.1, 6.5 In Tasks 1-8 you are asked to conduct some computations regarding this data. The computation should be carried out manually. All the steps that go into the computation should be presented and explained. (You may use R in order to verify your computation, but not as a substitute for conducting the manual computations.) A Random...
Question 1 Snowfalls occur randomly and independently over the course of winter in a Nebraska...
Question 1 Snowfalls occur randomly and independently over the course of winter in a Nebraska city. The average is one snowfall every 3 days. a) What is the probability of 5 snowfalls in 2 weeks? Carry answer to the nearest ten-thousandths b) What is the probability of a snowfall today? Carry answer to the nearest ten-thousandths Question 2 After observing the number of children checking out books, a librarian estimated the following probability distribution of x,...
How can we assess whether a project is a success or a failure? This case presents...
How can we assess whether a project is a success or a
failure?
This case presents two phases of a large business transformation project involving the implementation of an ERP system with the aim of creating an integrated company. The case illustrates some of the challenges associated with integration. It also presents the obstacles facing companies that undertake projects involving large information technology projects. Bombardier and Its Environment Joseph-Armand Bombardier was 15 years old when he built his first snowmobile...
2 (20 polats) A lighting system is comprised of two lightbulbs work indepeedently. Manufacturer fested failure of these components and this failure is know n to oceur randomly with rate (.) of 0.5 per year (a) Define the lifetime random variable and its pdf function. What is the expected lifetime? What is the 80% (i.e., top 20%) lifetime years? (b) What is the probability that both lightbulbs are still functioning after 2 years? (Hint: calculate probability of one component functioning...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
4. Suppose a random number generator generates 20 numbers per second, where each number is drawn uniformly from the interval 9,10), independently of all other numbers. We are interested in the event that one of the drawn numbers is very close to Usain Bolt's 100m sprint world record, that is, that this number belongs to the interval (9.575, 9.585). (a) Suppose that the random number generator runs for 10 seconds. Use the Poisson approximation to estimate the probability that it...
Suppose we are analyzing data from the exponential distribution, which has density function f (y) = ò exp (-5y) for y > 0, depending on a single parameter δ > 0, The exponential distribution arises in reliability theory as the waiting time until failure of a system that is subject to a constant risk of failure δ. (a) Using a computer: plot f(y; δ) as a function of y when δ-1. What is the area under this curve, and why?...
(1 point) Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace the card, and draw another card. You repeat this process until you have drawn 15 cards in all. What is the probability of drawing at least 5 diamonds? For the experiment above, let X denote the number of diamonds that are drawn. For this random variable, find its expected value and standard deviation E(X)=( o=
(1 point) After 8:00pm on any Thursday, the amount of time a person spends waiting in line to get into a well- known pub is a random variable represented by X. Suppose we can model the behavior of X with the Exponential probability distribution with a mean of waiting time of 45 minutes. (a) Provide the value of the standard deviation of this distribution. Enter your answer to two decimals. ox= 45 II minutes (b) Suppose you are in line...
How can we assess whether a project is a success or a
failure?
This case presents two phases of a large business transformation project involving the implementation of an ERP system with the aim of creating an integrated company. The case illustrates some of the challenges associated with integration. It also presents the obstacles facing companies that undertake projects involving large information technology projects. Bombardier and Its Environment Joseph-Armand Bombardier was 15 years old when he built his first snowmobile...
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