Determine a poisson process with arrival rate, Marketing Management

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Determine a poisson process with arrival rate

Assignment:

Let x(t) be a Poisson process with arrival rate λ = 0.5 s^-1

a) Find the probability that x(t) has at least two arrivals in the interval (t₁, t₃) and exactly one of them lies in (t₂, t₃), where t₁ = 3 s, t₂ = 4 s, t₃ = 6 s.

b) With τ₁, τ₂, τ₃ three consecutive and ordered arrival times for x(t), find the probability P[τ₃ - τ₁ > 3s|τ₂- τ₁ = 1s].

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