Problem #8: A system consists of five components is connected in series as shown below.1234 5 ——As soon as one component fails, the entire system will fail. Assume that the components fail independently of oneanother.Problem #8(a):Problem #8(b):(a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 106weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean123 weeks. Find the probability that the system lasts at least 59 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 81% of all such systems lasts at least one year?Round your answer to 4 decimals.Answer in years,correct to 2 decimals

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Answered: Problem #8: A system consists of five…

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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mathematical statistics. Problem 2.
Problem 2. (Exercise 6, Section 9.5.7) According to the Department of Motor Vehicles (DMV), the entity in charge of providing driving licenses in the United States, it is illegal to drive with a blood alcohol content of 0.08% or more if you are 21 or older. In the DMV's guidelines to determine when a person is driving under the influence, which can be found at https://www.dmv.ca.gov/portal/dmv/detail/pubs/hdbk/actions_drink, it is indicated that fewer than five percent of the population weighing 100 pounds will exceed the 0.33 alcohol level. Assume this is accurate. If the Highway Patrol stops in a random day 200 unrelated cars where the individual weighs one hundred pounds, on a Friday night, what is the probability that six percent of more individuals stopped exceeds that 0 33 alcohol level?
Working problem 4.12: If the event is a number '5' tuming in rolling a die, simulate rolling a die for 1000 times with increments of 100 and explain how the law of large numbers will prevail. Working problem 4.13 : The data in the Table below was taken from the U.S. Census Bureau report titled "HINC-01. Selected Characteristics of Households, by Total Money Income in 2005" (http://www.census.gov/hhes www/cpstables/032010/hhinc/new01 001.htm) Income Under $20,000 $20,000 to < $40.00O $40,000 to < $60.00O S60,000 to < $80,000 $80,000 to < $100,000 Above $100,000 Households (thousands) 24,559 26,904 20.026 14,535 9,362 7,813 If a U.S. family is selected at random, Determine (a) The probability that the family selected has an annual income of less than $40,000 (b) The probability that the family selected has an annual income of $40,000 to less than $80,000 (c) The probability that the family selected has an annual income of more than $100,000 29
2. Two systems have a continuous load of 105 MW. Find the expected load loss (ELL) of each system if the generation is composed of : a. Six 20 MW hydro generating units each with an availability of 0.9. b. Five 25 MW thermal units each with an unavailability of 0.2.
Problem 3. (Exercise 8, Section 9.5.7) Resistors of a certain type have resistances that are exponentially distributed with parameter 1 = 0.04. An operator connects 50 independent resistors in series, which causes total resistance in the circuit to be the sum of individual resistances.
Only a, b, c please!! Thank you!!!
Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the following data: Assume that the suburb has a population of 808000 and is growing at a rate of 3000 per year. Assume that the city has a populatior of 1060000 and is declining at a rate of 15000 per year. In how many years will the populations of the suburb and the city be equal? What will the populations be when they are equal?
Freddy is the owner of Freddy’s fast fuel for Small Aircraft specializing in “Providing flight fit fantastic fuel” for small general aviation aircraft such as a Cessna 172. Freddy is experimenting with a fueling process involving new equipment and is trying to determine if the current process takes more time than the new process with the new equipment he is experimenting with. If the current process takes more time than the new process, Freddy will purchase some new, rather expensive fueling equipment to use across several small general aviation airports his company services. Freddy is comparing sample mean times to evaluate his hypothesis about the population (total number of aircraft fuel fill-ups). Over the period of a week, he took a random sample of fuel fill-up times using both the old and new processes. Using the information Freddy provided, you ran a t-test for independent samples. These are the results (α = .05). t-Test: Two-Sample Assuming Unequal Variance Current…
Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of discovering the disease in 97% of all afflicted individuals. Suppose further that when it is tried on healthy individuals, 5% of them are incorrectly diagnosed as having the disease. Finally, suppose that when it is tried on individuals who have certain other milder diseases, 10% of them are incorrectly diagnosed. It is known that the percentages of individuals of the three types being considered here in the populations at large are 1%, 96%, and 3%, respectively. Calculate the probability that an individual, selected at random from the population at large and tested for the rare disease, actually has the disease if the test indicates he is so afflicted.
8
Problem #7: A system consists of five components is connected in series as shown below. 5 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 109 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 128 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. What must that mean be (in years) so that 97% of all such systems lasts at least one year?
Question 6 Having studied Fixed Income Securities, you are now working as an analyst for a well known bond fund. Your manager asks you to replicate the JP Morgan T-Bond Index using a tracking error minimization approach. You are to replicate this index as closely as possible using a medium duration Treasury bond (M-BOND) and a long duration Treasury bond (L-BOND). These expire in approximately 7.15 years’ and 29.25 years’ time respectively. The following variance-covariance matrix, based on daily returns over the preceding six months, is given to you to use in your replication: Note: As usual, variances are given on the diagonal, e.g. the variance of M-BOND is 0.0042%. As usual, covariances appear in the non-diagonal elements, e.g. the covariance of M-BOND and L-BOND is 0.0057%. (a) Suppose the optimal weights for M-BOND and L-BOND are 0.7 and 0.3. Calculate the expected tracking error of the portfolio and explain how you interpret this number. (b) Calculate the correlation matrix…

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