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.