Given five arrivals by time 5,their locations are iid uniform on (0,5) before ordering,so the count by time 3 is Binomial(5,3/5),proving I. Given three arrivals by time 5,two more rate-one exponential waits are needed,with total mean 2. Hence the conditional mean fifth time is 5+2=7. **C**.
More Poisson and Birth-Death Processes questions
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…
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).…
GATE 2022 ST Q28– Calls arrive as a rate-one Poisson process per minute. Choose five two-minute intervals.…
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…
GATE 2021 ST Q47– Customers arrive as a rate-ten Poisson process. Independently each is male or female with…
GATE 2021 ST Q60– Visitors arrive at a park as a rate-one Poisson process. Each stays an independent…