Discuss the following problems:
Q1. The Hoylake Rescue Squad rceives an emergency ca; every 1,2,3,4,5 or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week:
|
Time Between Emergency Calls (hr)
|
Probability
|
|
1
|
.05
|
|
2
|
.10
|
|
3
|
.30
|
|
4
|
.30
|
|
5
|
.20
|
|
6
|
.05
|
|
|
1.00
|
a. Simulate the emergency calls for 3 days (note that this will require a "running" or cumulative, hourly clock), using the random number table.
b. Compute the average time between calls and compare this value with the expected value of the time between calls from the probability distribution. Why are the results different?
c. How many calls were made during the 3 day period? Can you logically assume that this is an average number of calls per 3 day period? If not, how could you simulate to determine such an average?
Q2. The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution:
|
Tine between arrivals (min)
|
Probability
|
|
1
|
.15
|
|
2
|
.30
|
|
3
|
.40
|
|
4
|
.15
|
|
|
1.00
|
a. Simulate the arrival of cars at the service station for 20 arrivals and compute the average time between arrivals.
b. Simulate the arrival of cars at the service station for 1 hour, using a different stream of random numbers from those used in (a) and compute the average time between arrivals.
c. Compare the results obtained in (a) and (b).