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Probability-Reminder

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Network Reliability

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSELECTRIC))

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Abstract

This chapter contains material which you certainly have learned some time ago and which is familiar to you. No doubt, you have met some elements of algebra of events, random variables, distribution function and have heard about binomial distribution. Among the material of this chapter is a fundamental Law of Total Probability which will be used further in our exposition. Maybe, the section of order statistics is new for you. This is not complex but very important material which will be used in introducing a cumulative destruction spectrum. Our advice–ignore the algebra and concentrate on the final results. The last section contains a few topics from statistics. They will be used to evaluate the relative error of Monte Carlo estimation procedures.

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References

  1. Samaniego, F. G. (2007). System signatures and their applications in engineering reliability. US: Springer.

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  2. Elperin, T., Gertsbakh, I. B., & Lomonosov, M. (1991). Estimation of network reliability using graph evolution models. Transactions on Reliability, 40(5), 572–581.

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  3. Bertsekas, D., & Tsitsliksis, J. (2008). Introduction to probability (2nd ed.). Belmont: Athena Scientific.

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  4. Ross S. M. (2019). Introduction to probability models (12th ed.). Cambridge: Academic Press.

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  5. Google: Basic statistics.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University, Beer-Sheva, Israel

    Ilya Gertsbakh

  2. Software Engineering Department, Shamoon College of Engineering, Beer-Sheva, Israel

    Yoseph Shpungin

Authors
  1. Ilya Gertsbakh
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  2. Yoseph Shpungin
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Corresponding author

Correspondence to Ilya Gertsbakh .

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© 2020 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Gertsbakh, I., Shpungin, Y. (2020). Probability-Reminder. In: Network Reliability. SpringerBriefs in Electrical and Computer Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-1458-6_1

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  • DOI: https://doi.org/10.1007/978-981-15-1458-6_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-1457-9

  • Online ISBN: 978-981-15-1458-6

  • eBook Packages: EngineeringEngineering (R0)

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