Show that the equilibrium distribution for x1 and x2, Basic Computer Science

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Show that the equilibrium distribution for x1 and x2

A process has two stages of service. Customers arrive in a Poisson process and are served first by a stage with negative exponential service with parameter µ and then by a stage with negative exponential service with parameter P. Let X₁(t) and X₂(t) denote the numbers in the stages at time t. Show that the equilibrium distribution for X₁ and X₂ consists of two independent geometric distributions.

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Basic Computer Science: Show that the equilibrium distribution for x1 and x2

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