Individuals join a club in accordance with a Poisson process with rate ?. Each new member must pass...

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Individuals join a club in accordance with a Poisson process with rate ?. 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 ?. Let N i (t) denote the number of club members at time t who have passed through exactly i stages, i = 1, . . . , k ? 1. Also, let N(t) = (N 1 (t ),N 2 (t), . . . , N k?1 (t)). (a) Is {N(t ), t _ 0} a continuous-time Markov chain? (b) If so, give the infinitesimal transition rates. That is, for any state n = (n 1 , . . . , nk?1) give the possible next states along with their infinitesimal rates. Sep 15 2014 06:32 AM

 

Solution ID:609226 | This paper was updated on 26-Nov-2015

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