Conditional on exactly one arrival in(0,3), its time is uniform on that interval. Its expected value is the midpoint1.5=3/2, B. The unconditional exponential waiting-time mean1/2 is irrelevant after conditioning on the interval count.
More Poisson and Birth-Death Processes questions
GATE 2020 ST Q51– A pure birth process has rates λn=2ⁿ,n≥0. Let T be time to grow from0 to5. Find256Var(T).
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