GATE 2023 ST – Question 62

Stochastic Processes · Poisson and Birth-Death Processes · 2 marks · Numerical answer

A birth–death process on {0,1,2,3} has birth rates (1,1,2,0) and death rates (0,1,1,1). If π is its unique stationary distribution,find π₀+2π₁+3π₂+4π₃ to two decimals.

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Correct answer: 2.70 to 2.90

Explanation

Detailed balance gives π₁=π₀·1/1=π₀,π₂=π₁·1/1=π₀,and π₃=π₂·2/1=2π₀. Normalization gives π=(1,1,1,2)/5. The weighted sum=(1+2+3+8)/5=**2.80**.

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