Question

Suppose that visits to a website can be modeled by a Poisson process with a rate 10 per hour. (10 points) What is the probability that there are more than or equal to 2 visits within a given 1/2-hour interval? A supervisor starts to monitor the website from the start of a new shift. Then, what the expected valuc of the time/waited by the supervisor until the 10th visit to the website during that shift?

suppose that visits to a website can be modeled by a Poisson process with a rate λ=10 per hour

(a) What is the probability that there are more than or equal to 2 visits within a given 1/2 hour interval

(b) A supervisor starts to monitor the website from the start of a new shift. then what is the expected value of time waited by the supervisor until the 10th visit to the website during that shift?

Answer 1

Answer:

Here X follows Poisson distribution parameter m= 10;

a) Please refer below screenshot for probability that there are more than 2 or more visit within 0.5 hour.

Solution 1 6) 2 0火ぐ. 2 e S

Prob (More than or equal to 2 visits within 1/2 hour) = 0.9596

b)

Here, Poisson distribution X has parameter m= 10 per hour

Expected value of X in Poisson distribution is m itself.

Therefore Expected value of of time waited by the supervisor until the 10th visit to the website is 1 hour or 60 minutes.