Reference no: EM133266095
Three types of jobs arrive at a computer server: • With probability p1, a type 1 job arrives, requiring an exponentially distributed service time T1 with parameter λ, i.e., fT1 (t1) = λe-λt1 ,
With probability p2, a type 2 job arrives, requiring a uniformly distributed service time T2 in the interval [0, T],
With probability p3 = 1 - p1 - p2, a type 3 job arrives, requiring a fixed service time T3 = K, where K < T.
(a) Find P(T1 ≤ K).
(b) Find P(T2 ≤ K).
(c) Find the probability that service time of an arbitrary job, arriving according to the distribution (p1, p2, p3), is less than or equal to K.
(d) If service time of a job is known to be less than or equal to K, what is the probability that it is a type 1 job?
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