The number of arrivals of a poisson process of rate

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Let N denote the number of arrivals of a Poisson process of rate λ over the interval (0, T). Given N = n, let S₁,..., S_n denote the corresponding arrival times. Prove that

Conclude that, given N(T ) = n, S₁,..., S_n are the order statistics of a collection of n uniform (0, T ) random variables

Reference no: EM131083562

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