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The time in hours during which an electrical generator is operational is a random variable with r...
7. [10 pts.] The time, in hours, during which an electrical generator is operational is a...
7. [10 pts.] The time, in hours, during which an electrical generator is operational is a random variable of interest. After many studies, engineers expect the electrical generator to be operational for 5 days. a. Define the cumulative density function for the random variable. b. What is the probability that a generator of this type will be operational for: i. ii. Less than 40 hours? Between 60 and 160 hours?
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume...
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 39% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage. (Round to four decimal places as needed.) b. Find the probability of having...
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume...
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 17% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage (Round to four decimal places as needed.) b. Find the probability of having...
—- Hospitals typically require backup generators to provide electricity in the event of a power outage....
—- Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 35% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. A. Find the probability that both generators fail during a power outage. (Round to four decimal places as needed.) B. Find the probability of...
Hospitals typically require backup generators to provide electricity in the event of a power outage. A...
Hospitals typically require backup generators to provide electricity in the event of a power outage. A certain hospital has two backup generators, so that power is still available if one of them fails during a power outage. These generators operate independently, so that if one backup fails, the failure will not affect the operation of the other generator. Assume that both emergency backup generators are the same make and model, which is known to fail 21% of the times when...
4. The amount of time T (in hours) that a certain electrical component takes to fail...
4. The amount of time T (in hours) that a certain electrical component takes to fail has an exponential distribution with parameter > 0. The component is found to be working at midnight on a certain day. Let N be the number of full days after this time before the component fails (so if the component fails before midnight the next day, N = 0). (a) What is the probability that the component lasts at least 24 hours? (b) Find...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this r...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours.
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
#1 ArcSite Electrical, which produces generators, purchases a component that is used in its generators directly from the supplier. The generator production operation requires a constant 1,000 compone...
#1 ArcSite Electrical, which produces generators, purchases a component that is used in its generators directly from the supplier. The generator production operation requires a constant 1,000 components per month. It costs S25 to place each order. The unit cost is S2.50 per component, and the quarterly per-component holding cost is 5% of the value of the component. ArcSite operates 250 working days per year and the component supplier has a lead time of 5 days. (a) What is the...
Suppose that the time, in hours, required to repair a heat pump is a random variable...
Suppose that the time, in hours, required to repair a heat pump is a random variable X that has a gamma distribution with the parameters α = 4 and β = 2. What is the probability that the average time to repair the following 40 pumps be more than 7.5 hrs? Write the result with up to 4 decimals.
Suppose that the time (in hours) that Adam spends on an untimed final exam follows an...
Suppose that the time (in hours) that Adam spends on an untimed final exam follows an exponential distribution with mean 1.75 hours, and the time that Ben spends on the same exam follows an exponential distribution with mean 2.25 hours. Assume that their times are independent of each other. Using appropriate notation for random variables and events: a) Determine the probability that Ben finishes in less than 2 hours. (Show your work; you may use either the pdf or cdf.)...
7. [10 pts.] The time, in hours, during which an electrical generator is operational is a random variable of interest. After many studies, engineers expect the electrical generator to be operational for 5 days. a. Define the cumulative density function for the random variable. b. What is the probability that a generator of this type will be operational for: i. ii. Less than 40 hours? Between 60 and 160 hours?
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 39% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage. (Round to four decimal places as needed.) b. Find the probability of having...
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 17% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage (Round to four decimal places as needed.) b. Find the probability of having...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours.
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
#1 ArcSite Electrical, which produces generators, purchases a component that is used in its generators directly from the supplier. The generator production operation requires a constant 1,000 components per month. It costs S25 to place each order. The unit cost is S2.50 per component, and the quarterly per-component holding cost is 5% of the value of the component. ArcSite operates 250 working days per year and the component supplier has a lead time of 5 days. (a) What is the...
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