A system consists of two subsystems connected in series, as shown in the following schematic illustration. Each subsystem consists of two components connected in parallel. The AB subsystem fails when both A and B have failed. The CD subsystem fails when both C and D have failed. The system fails as soon as one of the two subsystems fails. Assume that the lifetimes of the components, in months, have the following distributions: A: Exp(1), B: Exp(0.1), C: Exp(0.2), D: Exp(0.2).

a. Generate, by simulation, a large number (at least 1000) of system lifetimes.

b. Estimate the mean system lifetime.

c. Estimate the median system lifetime.

d. Estimate the probability that the system functions for more than 6 months.

e. Estimate the 90th percentile of system lifetimes.

f. Estimate the probability that the AB subsystem fails before the CD subsystem does.

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A B D