A system with three independent components works correctly if at least one
component is functioning properly. Failure rates of the individual components are λ1
= 0.0001, λ2 = 0.0002, and λ3 = 0.0004 (assume exponential lifetime distributions).
(a) Determine the probability that the system will work for 1000 hours.
(b) Determine the density function of the lifetime X of the system.
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