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MA3710 Homework #3b 1. (8 points) 1. The time between system crashes on a university computer...
QUESTION 6 The time to failure (in hours) of fans in a personal computer can be...
QUESTION 6 The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with rate 0.0005. Round your answers to 4 decimal places. (a) What proportion of fans will last at least 10000 hours? (b) What proportion of fans will last at most 8000 hours? QUESTION 7 Given the probability density function f(x)=(0.02^9 x^8*e^(-0.02x))/8! for x>0 and f(x)=0 otherwise. Determine the mean and variance of the distribution. Round the answers to the...
IV. Continuous Distribution: Normal Normal 1. The average time to complete a final exam in a...
IV. Continuous Distribution: Normal Normal 1. The average time to complete a final exam in a given course is normally distributed. With average of 80 min, and standard deviation of 8 minutes. For a certain student taken at random: to. What is the probability of finishing the exam in an hour or less? b. What is the probability of finishing the exam between 60 min and 70 min? Exponential 2. The time to fail in hours of a laser beam...
2. (15 points) Suppose the time between arrivals of university shuttles in a randomly selected station...
2. (15 points) Suppose the time between arrivals of university shuttles in a randomly selected station has an exponential distribution with the mean of 15 minutes. a. (7 points) What is the probability that one randomly chosen student waits more than 20 minutes for the bus in that specific station? (8 points) What is the probability that one randomly chosen student waits between 10 and 15 minutes for the bus in that specific station? b.
(15 points) A manufacturer is studying the length of time required by a maintenance team to...
(15 points) A manufacturer is studying the length of time required by a maintenance team to respond to reported failure of a specific machine in the plant. The plant manager wants to know the percentage of repair calls answered within 10 minutes. 2. The response time, X, measured in minutes is known to have an exponential distribution. For the exponential distribution, as λ increases what happens to the mean and variance of the distribution? 4 points) Draw a sketch of...
HOMEWORK ASSIGNMENT FOR PROJECT MANAGEMENT 13. An automation project has the following activities and related data Time (weeks)Crash Immed. Maximum Activity Prede- Opti- Most Cost/week Crashable...
HOMEWORK ASSIGNMENT FOR PROJECT MANAGEMENT 13. An automation project has the following activities and related data Time (weeks)Crash Immed. Maximum Activity Prede- Opti- Most Cost/week Crashable Mean Varice cessors mistic (a) Likely (m) mistic (c (S1000) Weeks E(t) V(t) C A 5 D A 4 E B1 F B1 G C,D,E 2 6 6 HF2 12 15 3 13a. (5 points) Compute the mean and variance of each activity and record them on the table above. 13b. (5 points) Develop...
1. (20 points total) (a) (10 points) You have 100 light bulbs whose lifetimes are modeled...
1. (20 points total) (a) (10 points) You have 100 light bulbs whose lifetimes are modeled by an indepen- dent exponential distribution with a mean of 8 hours. The bulbs are used one at a time, with a failed bulb being replaced immediately by a new one. i. (5 pointsUse the central limit theorem to approximate the probability that there is still a working bulb after 850 hours. ii. (5 points) Use the central limit theorem to approximate the probability...
3. The time to failure (Y , measured in hours) of fans in a laptop computer...
3. The time to failure (Y , measured in hours) of fans in a laptop computer is modeled using an exponential distribution with λ = 0.0002. (a) Graph the pdf of Y . Compute E(Y ) and var(Y ). Place an “×” on the pdf indicating where E(Y ) is. (b) What is the probability that a fan will fail before 6,000 hours? will survive at least 12,000 hours? (c) Only 1 percent of all fans’ lifetimes will exceed which...
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 e.df. given by Fy) - 1 - exp{-1}, if y> 0 0, elsewhere. (a) Find the p.d.ff(s) of Y and show that it is indeed a valid p.d.f[2] (b) Find the 30 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 200...
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 e.df. given by Fy) - 1 - exp{-1}, if y> 0 0, elsewhere. (a) Find the p.d.ff(s) of Y and show that it is indeed a valid p.d.f[2] (b) Find the 30 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 200...
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...
QUESTION 6 The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with rate 0.0005. Round your answers to 4 decimal places. (a) What proportion of fans will last at least 10000 hours? (b) What proportion of fans will last at most 8000 hours? QUESTION 7 Given the probability density function f(x)=(0.02^9 x^8*e^(-0.02x))/8! for x>0 and f(x)=0 otherwise. Determine the mean and variance of the distribution. Round the answers to the...
2. (15 points) Suppose the time between arrivals of university shuttles in a randomly selected station has an exponential distribution with the mean of 15 minutes. a. (7 points) What is the probability that one randomly chosen student waits more than 20 minutes for the bus in that specific station? (8 points) What is the probability that one randomly chosen student waits between 10 and 15 minutes for the bus in that specific station? b.
(15 points) A manufacturer is studying the length of time required by a maintenance team to respond to reported failure of a specific machine in the plant. The plant manager wants to know the percentage of repair calls answered within 10 minutes. 2. The response time, X, measured in minutes is known to have an exponential distribution. For the exponential distribution, as λ increases what happens to the mean and variance of the distribution? 4 points) Draw a sketch of...
HOMEWORK ASSIGNMENT FOR PROJECT MANAGEMENT 13. An automation project has the following activities and related data Time (weeks)Crash Immed. Maximum Activity Prede- Opti- Most Cost/week Crashable Mean Varice cessors mistic (a) Likely (m) mistic (c (S1000) Weeks E(t) V(t) C A 5 D A 4 E B1 F B1 G C,D,E 2 6 6 HF2 12 15 3 13a. (5 points) Compute the mean and variance of each activity and record them on the table above. 13b. (5 points) Develop...
1. (20 points total) (a) (10 points) You have 100 light bulbs whose lifetimes are modeled by an indepen- dent exponential distribution with a mean of 8 hours. The bulbs are used one at a time, with a failed bulb being replaced immediately by a new one. i. (5 pointsUse the central limit theorem to approximate the probability that there is still a working bulb after 850 hours. ii. (5 points) Use the central limit theorem to approximate the probability...
Problem 7: (8 points) The length of time to failure (in hundred of hours) for a transistor is a random variable Y with e.df. given by Fy) - 1 - exp{-1}, if y> 0 0, elsewhere. (a) Find the p.d.ff(s) of Y and show that it is indeed a valid p.d.f[2] (b) Find the 30 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 200...
Problem 7: (8 points) The length of time to failure (in hundred of hours) for a transistor is a random variable Y with e.df. given by Fy) - 1 - exp{-1}, if y> 0 0, elsewhere. (a) Find the p.d.ff(s) of Y and show that it is indeed a valid p.d.f[2] (b) Find the 30 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 200...
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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