*7. Individuals join a club in accordance with a Poisson process with rate A. Each new member...
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*7. Individuals join a club in accordance with a Poisson process with rate A. Each new member must pass through k consecutive stages to become a full member of the club. The time it takes to pass through each stage is exponentially distributed with rate ì. Let Í((ß) denote the number of club members at time / that have passed through exactly / stages, / =
1 AT — 1. Also, let N(0 = (Nx(t),N2(t), ...,Nk_x(t)).
(a) Is {N(0, / > 0} a continuous-time Markov chain?
(b) If so, give the infinitesimal transition rates. That is, for any state
ç = («!,..., nk_x) give the possible next states along with their infinitesimal rates.
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