Suppose that a queueing system has two servers, an exponential interarrival time distribution with a mean of 2 hours, and an exponential service-time distribution with a mean of 2 hours for each server. Furthermore, a customer has just arrived at 12:00 noon. (a) What is the probability that the next arrival will come (i) before 1:00 P. M., (ii) between 1:00 and 2:00 P. M., and (iii) after 2:00 P. M.?

What is the probability that the next arrival will come (i) before 1:00 P.M = 0.3935

between 1:00 and 2:00 P.M. = 0.2387

after 2:00 P.M= 0.3679

Step-by-step explanation:

Let T be inter arrival time. Tn exponential = λ = 2

Si be service time. i = 1, 2. SIn exponential= ∪ = ,

Arrival of first customer: 12:00

(a) What is the probability that the next arrival will come (i) before 1:00 P.M., (ii) between 1:00 and 2:00 P.M., and (iii) after 2:00 P.M.?

i) P(T < 1) = F(1) = 1 - ε * = 0.3935

ii) P(1 < T < 2) = F(2) - F(1) = (1 -ε) -  (1 -ε)

= 0.2387

iii) P( T > 2) = ε = 0.3679

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this