Extend the model of Fig. 3.11 to n states. If all the transition probabilities are equal, show that the state probabilities follow the Poisson distribution. (This is one way of deriving the Poisson...

Extend the model of Fig. 3.11 to n states. If all the transition probabilities are equal, show that the state probabilities follow the Poisson distribution. (This is one way of deriving the Poisson distribution.). Hint: use of Laplace transforms helps in the derivation.