GATE Stochastic Processes: Poisson and Birth-Death Processes – Previous Year Questions
9 GATE previous year questions on Poisson and Birth-Death Processes (Stochastic Processes, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q47 – Customers arrive as a rate-ten Poisson process. Independently each is male or female with probability 1/2. Let N(t) count all arrivals,M(t) males,and…
- GATE 2021 ST Q60 – Visitors arrive at a park as a rate-one Poisson process. Each stays an independent Exp(rate 1) time,independent of arrivals. Currently 10 visitors are…
- GATE 2022 ST Q12 – A linear pure-death process on 0,…,N has death rates μ i=5i,N≥1. Write p i(t)=P(X(t)=i). Which forward equations and initial conditions are correct?
- GATE 2022 ST Q28 – Calls arrive as a rate-one Poisson process per minute. Choose five two-minute intervals. Let p be the probability each interval has at most one call.…
- GATE 2022 ST Q32 – X(t) is a Poisson process with P(X(t)=n)=e(−4t)(4t)n/n!. If C(t₁,t₂) is its covariance function,find C(5,3),as an integer.
- GATE 2023 ST Q38 – N(t) is a rate-one Poisson process. I:P(N(3)=3 N(5)=5)=binom(5,3)(3/5)³(2/5)². II:if S₅ is the fifth-arrival time,E(S₅ N(5)=3)=7. Which hold?
- GATE 2023 ST Q62 – 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…
- GATE 2025 ST Q17 – N(t) is a Poisson process of rate 2. Let X=N(6)−N(1),Y=N(5)−N(3),W=N(6)−N(5),Z=N(3)−N(1). Which holds?
- GATE 2026 ST Q55 – N(t) is a homogeneous Poisson process of rate 3 and T₁ its first arrival time. Which hold?