A system consists of five components is connected in series as shown below.235As soon as one component fails, the entire system will fail. Assume that the components fail independently of oneanother.(a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 91weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean121 weeks. Find the probability that the system lasts at least 50 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 94% of all such systems lasts at least one year?

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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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13.) A string of Christmas lights contains 20 lights. The lights are wired in series, so that if any light fails, the whole string will go dark. Each light has probability 0.98 of working for a 3- year period. The lights fail independently of each other. Find the probability that the string of lights will remain bright for 3 years.
Imagine an animal that shows two variants; one long-legged and one short-legged. Each female produces 2 female offspring per generation and then dies. The offspring of the long-legged ones survive to adulthood (reproductive age) with a probability of 55% and the offspring of the short-legged ones survive to adulthood with a probability of 45%. If you begin with a population of 60 females of each type, what proportion of individuals will have long legs in 5 generations? (Note that you can ignore males and count only females and their offspring.) Show all work.
A fair coin flipped 3 times in a row.Find the probably of the coin coming up tails at least twice
An analyst is presented with lists of 4 stocks and 5 bonds. He is asked to predict, in order, the 2 stocks that will yield the highest return over the next year and the 2 bonds that will have the highest return over the next year. Suppose that these predictions are made randomly and independently of each other. What is the probability that the analyst will be successful in at least 1 of the 2 tasks?
Assume that the batter hits with probability 0.2 against left-handed pitchers, and with probability 0.3 against right-handed pitchers. Both situations are Bernoulli processes. One month the player bats 22 times against left-handed pitchers and 52 times against right-handed pitchers. How many hits should the batter expect to get during this month?
Covid-19 returns a positive result 60% of the time if the individual tested is infected. The same disease returns a negative result 99% of the time if the individual tested is not infected. To ensure better results, Sarah is tested twice over the span of a few days. Assume that the tests are independent and that the individual has a 10% pre-test probability of being infected based on her symptoms. What is the probability that the said individual is infected given that she tested negative twice?
Each of the numbers 0 - 9 is written on a sheet of paper and the ten sheets of paper are placed in a box If two of these sheets of paper are selected from the box at random, without replacement, find the probability that both numbers are greater than 7.
116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that…
A couple wants to have 2 boys and 2 girls. They will continuous to have children until they have reached the goal.Assuming that the probability that they have 54% chance to have a boy and 46% chance to have a girl in every pregnancy. No twin or more are possible. Assuming that their goal is possible and has been fulfilled today! What is the probability that they have exactly two boys? What is the probability that they have exactly two girls? What is the probability that they have more than 4 children? What is the probability that they have in between 3 and 5 boys? What is the expected value of the number of children they have?
Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85. B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. D) The probability of surviving 1 year…

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