Messages arrive to a service facility at a Poisson rate of four messages per second.
(a) Write down an expression for the probability of at least two messages in a 2-s interval. Messages arrive at times T1, T2, … , where t = 0 is the beginning of the interval.
(b) Write down an expression for the probability that the first two arrivals occur before 2 s have elapsed. Suppose that four messages have arrived in the first 2 s.
(c) What are the mean and the variance of the number of messages that have arrived in the interval (1.5, 2.0)?
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