VLSI chips, essential to the running of a computer system, fail in accordance with a Poisson distribution with a mean of 1 chip every 5 weeks If there are two spare chips on hand (thus, the system will be down due to lack of chips if the number of defective chips exceeds 2), and if anew supply will arrive in 8 weeks, find:The probability that during the next 8 weeks, the system will be down due to lack of chips?If10 such systems are available, find the probability that exactly 3 systems will be
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Consider an infinite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. Let X(t) denote the number of customers in the system at time t. Find (a) E[X(t s) |X(s)=n] ; (b) Var[X(t s) |X(s)=n]. Hint: Divide the customers in the system at time t s into two groups, one consisting of "old" customers and the other of "new" customers. (c) Consider an infinite server queuing system in which custo
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An airport shuttle bus picks up all passengers waiting at a bus stop and drops them off at the airport terminal; it then returns to the stop and repeats the process. The times between returns to the stop are independent random variables with distribution F, mean μ, and variance σ^2. Passengers arrive at the bus stop in accordance with a Poisson process with rate λ. Suppose the bus has just left the stop, and let X denote the number of passengers it picks up when it returns. (a) Find E[X]. (b) Fi
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