Let (N(t) : be a Poisson process with rate 1. Let Tn denote the arr...

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Let (N(t) : be a Poisson process with rate 1. Let Tn denote the arrival time of the n-th customer. N(t) denotes the number of customers that have occurred by time t. Explicitly compute the following quantities. a) If the first customer arrives at time 6, what is the expected number of arrivals between time 5 and time 10? i.e. E(N(10) - N(5)IT1 = 6). b) If 12 customers have arrived from time o to time 6, what is the expected number of arrivals between time 5 and time 10? i.e. E(N(10) - N(5)IN(6) = 12) .

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