Question: A death process with state space (mathbf{Z}={0,1,2, ldots}) has death rates [mu_{0}=0, mu_{1}=2, text { and } mu_{2}=mu_{3}=1] Given (X(0)=3), determine (p_{j}(t)=P(X(t)=j)) for (j=0,1,2,3).

A death process with state space \(\mathbf{Z}=\{0,1,2, \ldots\}\) has death rates

\[\mu_{0}=0, \mu_{1}=2, \text { and } \mu_{2}=\mu_{3}=1\]

Given \(X(0)=3\), determine \(p_{j}(t)=P(X(t)=j)\) for \(j=0,1,2,3\).

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