Question: Consider a homogeneous Poisson process N t with a rate of . The time unit is an hour. Given that there were three arrivals during

Consider a homogeneous Poisson process N_t with a rate of λ. The time unit is an hour. Given that there were three arrivals during the first three hours, find the probability that

(a) All three occurred during the first hour;

(b) At least one arrival occurred during the first hour. Consider the general case and find the distribution of N_t given N_t+s = n. Does the answer depend on λ?

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