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 94weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean126 weeks. Find the probability that the system lasts at least 57 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 86% of all such systems lasts at least one year?

From the given information,There are 5 components connected in series.The first two components have…

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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QUESTION 3It has been established that soccer ace Fernandes chances of scoring a penalty is 70 percent all thetime. However, he is a streak shooter, and if he scores on one shot, his probability of scoring it on thepenalty shot immediately following is 0.85. But it has also been pointed out that another soccer starZlatan chances of scoring a goal in any game is 65 percent all the time. However, since he is a streakstriker, and if he scores in one game, his probability of scoring in the game immediately following is0.75.3.1.Write this in the probability notation. 3.2.Calculate the probability that Fernandes will score the penalties on two consecutive shots. 3.3.Calculate the probability that Fernandes scores a penalty because Zlatan has scored twice. 3.4.Are probabilities that Zlatan scores in second game and that he scores in the third gameindependent in this question? Explain.
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
A poker player has either good luck or bad luck each time she plays poker. She notices that if she has good luck one time, then she has good luck the next time with probability 0.2 and if she has bad luck one time, then she has good luck the next time with probability 0.4. What fraction of the time in the long run does the poker player have good luck?
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?
Answer all of these please
Please provide steps for how you got the solution to the problem provided below. A machine is used to produce one of each of two types of product (A and B) on alternating days, i.e., if A is produced today then B will be produced tomorrow and vice versa. Each day, there is a probability that the machine malfunctions. Malfunction probability after a day of operation is 0.03 when producing A and 0.07 when producing B. Once the machine malfunctions, it is no longer operable and will not be replaced until sometime in the future (beyond modeling horizon). Model the system as a Markov chain (give transition matrix on your paper). Suppose that on Monday product A was produced. Find the probability that the machine is still operable by the morning of Thursday. Your model should have a state ”malfunction”, which cannot transition to any other state other than itself.
Suppose the probability of getting the flu is 0.20, the probability of getting a flu shot is 0.60, and the probability of bothgetting the flu and a flu shot is 0.10. (a) Find the probability of the union between (getting the the flu) and (getting the flu shot).
Suppose the weather moves between three states 1,2,3. It stays in state 1 for an exponentially distributed number of days with mean 3, then goes to state 2. It stays in state 2 for an exponentially distributed number of days with mean 4, then goes to state 3. It stays in state 3 for an exponentially distributed number of days with mean 1, then goes to state 1. Compute the long-term probability that the weather is in state 1. Write your answer as a decimal.

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