4. A parallel system functions whenever at least one of its components works. Suppose you have...
A parallel system consisting of 4 independent components works if at least one component works. However, a seriesl system consisting of 4 independent components works if all components work. Now suppose probability p of any component works is 0.5. Compute the following quantity and interpret your results.
please help ... 4-23 The guidance system design of a satellite places several components in parallel. The system will function as long as at least one of the components is operational. In a particular satellite, 4 such components are placed in parallel. If the probability of a component operating successfully is 0.9, what is the probability of the system functioning? What is the probability of the system failing? Assume that the components operate independently of each other.
Question 4 [20 marks] A system consists of five components in two branches as shown in the following diagram: C-D-E- In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities: P(A fails) = P(B fails) = 0.1 and P(C fails) = P(D fails) = P(E fails) = 0.2. (a) What is the probability that the system works? (b) Given that the...
8 (10 polints) A ystem conslists of 4 components ln a eries, so the system works properly if all of the for 1- 1,2,3,4 components are functional. In other words, the system fails if and only If at least one of its components als Suppose the probability that the component falils is less than or equal to p Flad n pper bound on the probability that the syetem fails 6. (10 points) A system consists of 4 components in a...
An electronic control system contains 10 components that work independently of one another, and is capable of working normally if at most two components fail. Due to unfavorable climate conditions, each component has a failure probability of 20%. What is the probability that the system as a whole works?
A circuit system is given in the following figure, where the number in each component represents the probability that the component works. Assume the components fail independently. (a) What is the probability that the entire system work? (b) Given that the system works, what is the probability that the component A is not working? 0.7 0.7 0.8 0.8 0.8
Suppose 4 components of system all act independently, and each fails within a year 10% of the time. Find the probability none fails within a year Find the probability at least one fails within a year Find the probability all fail within a year. Find the probability at least one works the entire year.
Suppose a computer system is assembled out of 100 components, and these are completely assembled before the power is ever applied. Assume that the computer fails to work properly if any component fails a) the rate of defects or each component of the system is only 0 22%, what is the probability that the assembled computer works when switched on, assuming the components are independent? b) For the probability that the system works to be 99% what is the largest...
5. A system consisting of n components is said to be a k-out-of-n system (ksn) if the system functions during a given mission time if and only if at least k of the n components function. Suppose that all components function independently of each other. a) If the ith component functions with probability P, i-1,2,3 derive the formula for the probability that a 2-out-of-3 system functions. b) Repeat part a) for a 3-out-of-4 system. c) Calculate the probability that the...
A system consists of five identical components connected in series as shown:As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one another. Define eventsAi= {ith component lasts at least t hours}, i = 1, . . . , 5, so that the Ais are independent events. Let X = the time at which the system failsthat is, the...