Events occur according to a Poisson process with rate A = 2 per hour. What is th

Question

Events occur according to a Poisson process with rate A = 2 per hour. What is the probability that no events occur between the times of 8 A.M. and 10 A M ? What is the expected value of the number of events that occur between the times of 8 A.M. and 10 A.M If we Mart counting events at 8 AM . what time of day If the 5th event expected? If we know the 10th event expected? If we know the 10th event occurred at 3 P.M., What is the probability that the 11th event will occur before 4 P.M.? If we know the 10th event occurred at 3 P.M., what is the probability that the 12th event will occur after 4 P.M?

Explanation / Answer

event occur according to poisson process with rate = 2 per hour

a) what is the probability that no event between 8am and 10 am

we need,    we have = 2 per hour and t = 2 hours.

thus

P(X=0) = e^(-t)(t)^0 / 0! = e^(-2*2) = e^-4 = 0.0183       = 1.8 %

thus ans.

b) what is expected no of events occur that between times of 8 am and 10 am ?

Expectation = t = 2*2 = 4

c)event occur according to poisson process with rate = 2 per hour

thus per hour we will expect 2 events

so in 2 hours we will expect 4 events

so in 3 hours we will expect 6 events

thus if we start couting events at 8AM

before 9 AM 2 events will be occured

before 10 AM 4 events will be occured

before 11 AM 6 events will be occured

thus we can expect 5th event between 10AM and 11 AM

d)10th event occured at 3PM

what is the probability that 11th occured before 4 PM.?

since wecan expect 2 event per hour.

probability that 11th event occur before 4 pm is 1.        (infact 2 events will occur before 4pm 11th and 12th)

e)

what is the probability that 12th occured before 4 PM.?

since wecan expect 2 event per hour.

probability that 12th event occur before 4 pm is 1.        (infact 2 events will occur before 4pm 11th and 12th)

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