Question: Consider a Poisson input process where the arrival rate is 4/hour. Consider N1 = number of arrivals between 1pm and 3pm, N2 =number of arrivals

Consider a Poisson input process where the arrival rate is 4/hour.

Consider N1 = number of arrivals between 1pm and 3pm, N2 =number of arrivals between 2pm and 4pm.

Compute the probability that N2 = 8, given that N1 = 4.

Hint: N1 and N2 are not independent since they have the time window from 2pm to 3pm in common.

You need to decompose the counts so that no time window is shared, so that the counts become independent.

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