Question

 Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter u= 8t.  (Round youranswers to three decimal places.) 

(a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? 

     What is the probability that at least 6 small aircraft arrive during a 1-hour period? 

     What is the probability that at least 12 small aircraft arrive during a 1-hour period? 

(b) What is the expected value and standard deviation of the number of small aircraft that arrive during a 75-min period? 

(c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? 

     What is the probability that at most 12 small aircraft arrive during a 2.5-hour period?

Answer 1

M=8f A Ans: Gren data, x = 2 = 8 per hour, porssion probability P(x-x) P (x = x) = 1-8 (Xex) ! X-1 - I- E x ! x=0 10.112 10 =) - E x=0 x ! D 8 x 75 = 110 - 60 Expected value standard deviation - Vio 3.162 c) for a 2.5 how period, aug no. of no of arrivals 20 arrrals 2.5x8 - P(x220) 99 20 2 I E e (20) = 10.530 x=0 R! } (x412) { 12 2 a E 0039 X=0 !