Consider a system with n capacitors in parallel. For the system to function prop-erly

Chapter 1, Problem 9

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Consider a system with n capacitors in parallel. For the system to function prop-erly, at least k-out-of-n capacitors should be functioning properly. A capacitorcan fail in two modes: open and short (circuit). If a capacitor develops an opencircuit, and the number of remaining working capacitors is greater than or equalto k, then the system still functions properly. If any one capacitor develops ashort circuit then the system fails immediately. Given the probability of a capaci-tor functioning properly p1=0.3, the probability of a capacitor developing a shortcircuit p2=0.4, the probability of a capacitor developing an open circuit p3=0.3,n=10 and k=7, calculate the probability of the system functioning properly.10. Consider an example of n nonhomogeneous Bernoulli trials where a failure canoccur on each trial independently, with a probability 1 ei for the ith trial[KOVA 2000]. Prove that over n trials,(a) P(no failure occurs) = e[n(n+1)/2].(b) P(no more than one failure occurs) = e[n(n+1)/2]ee(n+1)1e n + 1