Question

Problem 2. Customers arrive at a call center according to a Poisson process with rate 6/. (a) Find the probability that the 5th call comes within 10 minutes of the 4th call. (b) Find the probability that the 9th call comes within 15 minutes of the 7th call.

Answer 1

Solutions finom given data Let, NCH) be the poission process with rate 6/ h P{wick) = n3 = 164/7)". i n :0,1,2.... ; P& nuck+s) = miness = ns = p< wilt) = m-n} cas find the probability that the 5th call comes within 10 minutes of the 4th call. P{N(18+5) = 5 & Nes) = 4} :P {N(10)=1} = (60/a) ebolu = (19.0986) e 19.0986 9.64x108 0.000000097 =0.000000097 .: So, the Sequired probability * --> 0.000000097 (bo find the probability that the 9th call comes within 15 minutes of the 7th call?

= P& N615 +S) = ( wk99 = 73 = P{N(15) = 2 Ź (20.je-9017 = 0.5 * 820.7016 * e-90/70 I 1.48% 1070 N 0-00000000015 0.00000000015 .. so the grequlred probability in -> 0.00000000015, .