3.Consider the problem of computing reliability of so-called seriesparallel systems. A seriessystem is one in which all components are so interrelated that the entire system will fail if any one of its components fails. On the other hand, a parallel system is one that will fail only if all of its components fail. If a system consists of n components, and for f = 1, 2,, n, we define events A; = "component i is functioning properly." Let the reliability, Ri, of component i be dened as the probability that the component is functioning properly; then R;- = P(Aj). Find the system reliability of: a. The Series System (Hint: Use ofintersection of the independent events AIS). b. The Parallel System (Hint: First nd the failure of the system by using intersection of complements of the independent events As, as the parallel system fails if all n components will fail. Finally, subtract the result from 1 to get the reliability). 4Consider a series-parallel system of n serial stages where stage i consists of n: identical components in parallel. Let the reliability of each component at stage i be Ri. Assuming that all components are independent, show that the system reliability Rsp is given by: :l'l[1*(1* )] Moreover, nd the reliability of the system shown in Figure, consisting of ve stages, with m = n2 = r15 = 1, and n3 = 3 and m = 2. Also, R1 = 0.95, R2 = 0.99, R3 = 0.70, R4 = 0.75, and R5 = 0.9. \"MHEE (Hint: Apply the results of Problem (3) to prove the given Eqn.)