Question: A birth- and death process has state space (mathbf{Z}={0,1, ldots, n}) and transition rates [lambda_{j}=(n-j) lambda text { and } mu_{j}=j mu ; j=0,1, ldots,

A birth- and death process has state space \(\mathbf{Z}=\{0,1, \ldots, n\}\) and transition rates

\[\lambda_{j}=(n-j) \lambda \text { and } \mu_{j}=j \mu ; j=0,1, \ldots, n\]

Determine its stationary state probabilities.

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