Question: Suppose that a certain system contains a key component #1 which has an identical backup component # 2 in an "off " state until needed.

Find a) the p.m.f. (p.d.f.) of a lifetime X of a system

b) find \(E\left( X \right)\) and

c) determine the probability that the system will not fail before 1,800 hours

if the length of life of a component X _i , i = 1, 2, measured in thousand of hours has

1. a discrete distribution
   
2. a uniform distribution on the interval [0, 3].

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