Problem #7: A system consists of five components is connected in series as shown below.5As soon as one component fails, the entire system will fail. Assume that the components fail independently ofone another.(a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 109weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean128 weeks. Find the probability that the system lasts at least 49 weeks.(b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. Whatmust that mean be (in years) so that 97% of all such systems lasts at least one year?

first two component have lifetime that are exponentially distributed with mean 109 weeks last three…

Answered: A system consists of five components is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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solve with steps Three different machines A1, A2, A3 were used for the producing a large batch of similar manufactured items. Suppose that 10% of items are produced by machine A1, 20% by A2 and 40% by A3. Suppose further that 1%of the items produced by A1, 2% by A2 and 3% by A3 machine are defective. Suppose one item is selected from the entire batch and it is found to be defective. Calculate the probability that this item was produced bymachine A2
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Two geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.7551
5
Suppose the average tread-life of a certain brand of tire is 45,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life between 30,000 and 50,000 miles?
A certain tennis player makes a successful first serve 78% of the time. Assume that each serve is independent of the others. If she serves 9times, what's the probability she gets: Part 1 a) The probability that she gets all 9 serves in is _______________ (Round to three decimal places as needed.). Part 2 b) The probability she gets exactly 4 serves in is _______________ (Round to three decimal places as needed.) Part 3 c) The probability she gets at least 7 serves in is ______________________ (Round to three decimal places as needed.) Part 4 d) The probability that there are no more than 6 serves in is __________ (Round to three decimal places as needed.)
6. A small company can employ 3 workers. Each worker independently stays on the job for an exponentially distributed time with a mean of one year and then quits. When a worker quits, it takes the company an exponentially distributed time with a mean of 1/10 of a year to hire a replacement for that worker (independently of how long it takes to replace other workers). If the company takes in $1000 per day in revenue when it has 3 workers, $800 per day when it has 2 workers, and $500 per day when it has 0 or 1 workers, what is the company's long-run average daily revenue?
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