Two independent components placed in series

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A machine is made up of two independent components placed in series. The lifetime of each component is uniformly distributed over the interval [0,1]. As soon as the machine breaks down, the component that caused the failure is replaced by a new one. Let N(t) be the number of replacements in the interval (0,t].

(a) Is the stochastic process {N(t), t ≥ 0} a continuous-time Markov chain? Justify.

(b) Is {N(t),t ≥ 0} a renewal process? Justify.

(c) Let 5i be the time of the first replacement. Calculate the probability density function of Si.

Reference no: EM131130672

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