Question

QUESTION 9 An old house in Fayetteville is inhabited by a variety of ghosts. Ghost appearances occur in the house according to a Poisson process having a rate of 2 ghosts per hour. A professor from Transylvania University has developed a device which can be used to detect ghost appearances. Suppose we began observing the facility at 8:00 a.m. It is now 1:00 p.m., and the last ghost appearance (the 5th overall) was at 12:45 p.m. From this moment, how long on average (in hours) does it take for the 7th ghost to appear? ( Report answer to three decimal places. Answer must be within +/- 0.001 of correct value.) QUESTION 10 An old house in Fayetteville is inhabited by a variety of ghosts. Ghost appearances occur in the house according to a Poisson process having a rate of 1.5 ghosts per hour. A professor from Transylvania University has developed a device which can be used to detect ghost appearances. Suppose 4 ghosts appeared between 7:00 a.m. and 9:00 a.m What is the probability that 9 ghosts appear between 7:00 a.m. and 3:00 p.m.? ( Report answer to three decimal places. Answer must be within +/- 0.001 of correct value.)

Answer 1

Q 9

Ghost appearances occur in the house according to a Poisson process having a rate of 2 ghosts per hour. Suppose we begin observing the facility at 8:00 a.m and it is now 1:00 p.m., and the last ghost appearance was at 12:45 p.m. The expected value of the 7th ghost's appearance time is

Mean = 2*5 = 10 ghosts apperin 5 hour

But 5th apper at 12:45 p.m i.e every 3 minutes 1 ghost is apper

average time is 3 minutes

Q 10

Mean = 1.5*8 = 12.0

Then, the probability that 9 ghosts appear between 7:00 a.m. and 3:00 p.m.

$\small P(X=9)=e^{-12}\frac{12^{9}}{9!}=0.087364$

11.

Mean =1.3*3/4 = 0.975

the probability that less than 3 ghosts appear between 10:30 p.m. and 11:15 p.m is

$\small P(X<3)=\sum_{x=0}^{2}e^{-0.975}\frac{0.975^{x}}{x!}=0.924$