You and your roommate share 1 iPhone. Calls arrive according to a Poisson process at rate: 10 per hour.

With probability p = 0.40 any such call is, independently, for you; otherwise (probability q = 1 - p = 0.6) for your roommate.

1) What is the expected value and variance of the number of calls that you receive by time t = 2 hours? What is the expected value and variance of the number of calls that your roommate receives by time t = 2 hours?

2) What is the probability that your roommate receives 5 calls before you receive your first one?

3) What is the probability that you receive 4 calls between 2 and 4 PM, and 2 calls between 5 and 7 PM?

4) Given that you received 14 calls between 2 and 4 PM, what is the probability that your roommate received only 1 call during that same time interval?

5) Given that you received 14 calls between 2 and 4 PM, what is the probability that your roommate received only 1 call between 5 and 7 PM?

6) Given that you received 1 call between 2 and 4 PM, what is the probability that it occurred between 2 and 2 : 30PM?

7) Given that you received 2 calls between 2 and 4 PM, what is the probability that they both occurred between 2 and 2 : 30PM?

8) Given that you received n >= 1 calls between 2 and 4 PM, what is the probability that they all occurred between 2 and 2 : 30PM?

Please explain answers.