In: Statistics and Probability
Suppose that there are two supervisors at Kardashian restaurant (Kim and Kylie), and the # of customer complaints differs based on the supervisor on duty. This is determined according to a Poisson process. The quality of service of one day does NOT affect the quality of service on the next day.
| 
 Supervisor on duty:  | 
 Average # of customer complaints (per day):  | 
 Days on duty (out of 5 days):  | 
| 
 Kim  | 
 2 per day  | 
 2 out of 5 days  | 
| 
 Kylie  | 
 3 per day  | 
 3 out of 5 days  | 
Answer the following questions based on the information given above:
i) Assuming that Kylie is on duty, solve for the expected # of customer complaints in the next 2 days.
ii) Assuming that Kylie is on duty, solve for the probability that there will be no customer complaints tomorrow.
iii) If there was AT LEAST 1 customer complaint yesterday, what's the probability that Kim was on duty?
iv) Solve for the probability that there will be no customer complaints in the next 2 days.