Answer:
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= ∪ = [tex]\frac{1}{2}[/tex] ,
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[tex]^-{\frac{1}{2}}[/tex] *[tex]^{1}[/tex] = 0.3935
ii) P(1 < T < 2) = F(2) - F(1) = (1 -ε[tex]-\frac{1}{2} * 2[/tex]) - (1 -ε[tex]-\frac{1}{2} * 1[/tex])
= 0.2387
iii) P( T > 2) = ε[tex]-\frac{1}{2} * 2[/tex] = 0.3679
