Question

Someone claims that the number of hits on his website has a Poisson distribution with mean three per half an hour. We would like to observe the website statistics during a period of two hours to figure out the number of hits during this period

a)Define the random variable of interest, its support, and parameter values over this period

b)What is the probability that number of hits will be at least 10 over this period

Answer 1

Solution:

a)

We are given that the number of hits on the website has a Poisson distribution with mean three hits per half an hour.

We know that in 2 hours there will be 4 half hours.

Let x be the number of hits on the website during a period of two hours. Then the random variable x has a Poisson distribution with mean as:

b)What is the probability that the number of hits will be at least 10 over this period

Answer: We have to find

We know that:

Now we can use excel to find this probability. The excel function is:

  

Therefore, we have: