### Component System Probability Analysis**Figure Description:**The figure illustrates a system of four components connected in a specific configuration, depicted by four labeled boxes connected by lines. The components are as follows:- **Components 1 and 2**: These are connected in parallel. In a parallel configuration, the subsystem functions correctly if at least one of the components is working.- **Components 3 and 4**: These are connected in series. In a series configuration, the subsystem functions only if both components are working.**Task:**Calculate the probability that the entire system works correctly, given:- Each component operates independently.- The probability of any given component working is $ P(\text{component working}) = 0.9 $.**Solution Approach:**1. **Parallel Configuration (Components 1 and 2):** - Probability that either Component 1 or 2 works: - $ P(\text{at least one works}) = 1 - P(\text{neither work}) $ - $ P(\text{neither 1 nor 2 work}) = (1 - 0.9)(1 - 0.9) = 0.1 \times 0.1 = 0.01 $ - $ P(\text{at least one works}) = 1 - 0.01 = 0.99 $2. **Series Configuration (Components 3 and 4):** - Probability that both Component 3 and 4 work: - $ P(\text{both work}) = P(\text{3 works}) \times P(\text{4 works}) = 0.9 \times 0.9 = 0.81 $3. **Entire System:** - Final probability that the entire system functions is the product of the probabilities of each subsystem functioning: - $ P(\text{system works}) = P(\text{1 and 2 parallel}) \times P(\text{3 and 4 series}) = 0.99 \times 0.81 = 0.8019 $Therefore, the probability that the entire system works correctly is **0.8019**.

We can divide the system in two parts.Parallel subsystem works (if either 1 or 2 work).Series…

Answered: Components 1 and 2 are connected in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For a parallel structure of identical components, the system can succeed if at least one of the components succeeds, Assume that components fail independently of each other and that each component has a 0.08 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It V be unusual to observe one component fail, since the probability that one component fails,, is V than 0.05. It V be unusual to observe two components fail, since the probability that two components fail,. is v than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) P Type here to search lyp
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A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for 10 Hollywood movies made in the past five years. Each movie was based on an epic novel. For these data, x1 = first-year box office receipts of the movie, x2 = total production costs of the movie, x3 = total promotional costs of the movie, and x4 = total book sales prior to movie release. All units are in millions of dollars. x1 x2 x3 x4 85.1 8.5 5.1 4.7 106.3 12.9 5.8 8.8 50.2 5.2 2.1 15.1 130.6 10.7 8.4 12.2 54.8 3.1 2.9 10.6 30.3 3.5 1.2 3.5 79.4 9.2 3.7 9.7 91.0 9.0 7.6 5.9 135.4 15.1 7.7 20.8 89.3 10.2 4.5 7.9 a) If x2 (production costs) and x4 (book sales) were held fixed but x3 (promotional costs) were increased by 1.1 million dollars, what would you expect for the corresponding change in x1 (box office receipts)? (Use 2 decimal places.)b) Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of…
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure. Complete parts (a) through (c) below. T.... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, than 0.05. It be unusual to observe two components fail, since the probability that two components fail,, is than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) O Time Remaining: 02:29:14 Next Left Raht
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