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1. A job shop consists of three machines and two repairmen. The amount of time a machine works before breaking down is exponentially distributed with mean 10. If the amount of time it takes a single repairman to ?x a machine is exponentially distributed with mean 8, then

(a) what is the average number of machines not in use?

(b) what proportion of time are both repairmen busy?

2. Consider a taxi station where taxis and customers arrive in accordance with Poisson processes with respective rates of one and two per minute. A taxi will wait no matter how many other taxis are present. However, an arriving customer that does not ?nd a taxi waiting leaves. Find

(a) the average number of taxis waiting, and

(b) the proportion of arriving customers that get taxis.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91721410

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