# MAT540 Week 3 Homework

**Topics:**Randomness, Random variable, Cumulative distribution function

**Pages:**2 (481 words)

**Published:**October 14, 2014

MAT540 Week 3 Homework

Chapter 14

1. The Hoylake Rescue Squad receives an emergency call 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

0.05

2

0.10

3

0.30

4

0.30

5

0.20

6

0.05

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? 2. The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution: Time Between

Arrivals (min.)

Probability

1

0.15

2

0.30

3

0.40

4

0.15

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).

3. The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week follows: Machine Breakdowns

per Week

Probability

0

0.10

1

0.10

2

0.20

3

0.25

4

0.30

5

0.05

1.00

a. Simulate the machine breakdowns per week for 20 weeks. b. Compute the average number of machines that will break down per week. 5. Simulate the decision situation described in Problem 16(a) at the end of Chapter 12 for 20 weeks, and recommend the best decision. Reference Problem 16(a) in Chapter 12: A concessions manager at the Tech versus A&M football game must...

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