Problem 2. (USE R) Suppose the arrival of telephone calls at a switch can be mod

Question

Problem 2. (USE R) Suppose the arrival of telephone calls at a switch can be modeled with a Poisson random variable, i.e., X, the number of calls that arrives in t minutes, is Poisson with parameter Xt, where X is the average arrival rate in calls/minute. Suppose that the average rate of calls is 10 per minute. (a) What is the probability that fewer than three calls will be received in the first 6 seconds? (b) What is the probability that at least six calls will be received in the first 30 seconds?

Explanation / Answer

Ans:

average rate=10 per minute=10/60 per sec=1/6 per sec

a)parameter=(1/6)*6=1

P(less than 3 calls)=e-1*(10/0!+11/1!+12/2!)=e-1*(1+1+0.5)=e-1*(2.5)=0.9197

b)parameter=(1/6)*30=5

P(at least 6)=1-P(less than 6)=1-e-5*(50/0!+51/1!+52/2!+53/3!+54/4!+55/5!)

=1-e-5*(1+5+12.5+20.83+26.04+26.04)

=1-0.6159

=0.3841

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.