An exponential random variable with mean

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A sequence of queries are made to a database system. The response time of the system, T seconds, is an exponential random variable with mean 8. As soon as the system responds to a query, the next query is made. Assuming the first query is made at time zero, let N(t) denote the number of queries made by time t.

(a) What is P[T ≥ 4], the probability that a single query will last at least four seconds?

(b) If the database user has been waiting five seconds for a response, what is P[T ≥ 13|T ≥ 5],

the probability that it will last at least eight more seconds?

Reference no: EM131083531

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