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A machine has 7 identical components that operate independently with respective lifetimes X1,X2,...,X7 hours. Their common PDF and CDF are fX(x) and FX(x), respectively. Find the probability that the machine lasts at most 5 hours if
a. It keeps going until all its components fail.
b. It fails as soon as one of its components fails.
c. It fails when it has only one component that has not failed.
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