Question: A system consists of five components. Suppose that the lifetimes of the components are independent, with exponential distributions EXP(1), . . . , EXP(5). Find

A system consists of five components. Suppose that the lifetimes of the components are independent, with exponential distributions EXP(λ1), . . . , EXP(λ5). Find the cdf and density of variable T = time to failure of the system if the components are connected:

(i) In series (see Figure 8.2), so that the system fails as soon as one of its components fails. (ii) In parallel (see Figure 8.3), so that the system works as long as at least one component is operating. (iii) As in Figure 8.4.

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