Part CCSIR NET December 2023competing-poisson-processes

Competing poisson processes

Suppose {X(t)} and {Y(t)} are two independent homogeneous Poisson processes with the same rate $λ = 2$ . Let $W_{n}$ ˣ and $W_{n}$ ʸ be the waiting times for the n-th arrival in each process. Which of the following statements are true?

A. $P (W_{2}$ ˣ $< W_{3}$ ʸ) = 11/16✓
B. $P (W_{1}$ ˣ $< W_{1}$ ʸ) = 1/2✓
C. $P (W_{2}$ ˣ $< W_{3}$ ʸ) = 13/16
D. $P (W_{1}$ ˣ $< W_{1}$ ʸ) = 1/4

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests dependence misread.

See pricing

50 are analysed free — try those first.

The trap it tests

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

Drill statements like this

Competing poisson processes

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