# National Open University Exam Past Question – CIT 412 MAY/JUNE 2012 EXAMINATION

## NATIONAL OPEN UNIVERSITY OF NIGERIA CIT 412 MODELLING AND SIMULATION

14-16 AHMADU BELLO WAY, VICTORIA ISLAND LAGOS SCHOOL OF SCIENCE AND TECHNOLOGY

MAY/JUNE 2012 EXAMINATION

CIT 412 MODELLING AND SIMULATION TIME ALLOWED: 3 HOURS

INSTRUCTION: ANSWER ANY FIVE QUESTIONS IN ALL

1a.        Enumerate six (6) properties of a good Random number generator.                   [6 marks]

1b.        Define the below graphs and show the data distribution of the below table in the bar   graph

and pie chart

• Bar graphs • Double bar graphs • Histograms and • Pie Charts use port. [7 marks]

 Name       value Olu           23 Ade          32 Ope          51 Tunde      67 James       12

 1c. State four (4) types of Simulations. [4 marks] 1d.   2a. Highlight the Advantages of using Model.   Briefly explain what is meant by a Model. [3 marks]   [5 marks]

2b.        Suppose we have a sample with the following 6 observations: 4, 5, 7, 2, 1, 2. Show your

workings by calculating the Measures of Central Tendency, Range and Standard

Deviation as Measures of Variation.                                                                        [10 marks]

2c.        Explain Queuing theory.                                                                                          [5 marks]

3a.        What is a Random Number?                                                                                   [3 marks]

3b.        State the Theorem of Multiplication of Probabilities.                                [9 marks]

3c.        Using Mixed Congruential formula, suppose m = 8, a = 5, c = 7 and X0 (seed) = 4,

generate a random sequence of integer numbers in a tabular form.                   [8 marks]

4a.        Discuss Poisson Process.                                                                                [6 marks]

4b.        Why simulation language?                                                                                      [10 marks]

4c.        What is the chances of generating any digits between 0, 1, 2,3,4,5,6,7,8, 9 as the nth        drawn

number from the given numbers 0-9  irrespective of all the preceding digits in   the  recorded  sequence of Pseudorandom Number Generation.             [4 marks]

5a.        Discuss Monte Carlo algorithm and highlight the methods used by the algorithm.

[7 marks]

5b.        Explain in detail the queuing disciplines and its four (4) methods/disciplines. [10 marks]

5c.        Write a simple QBASIC program that will stimulate the tossing of two dice and display the value obtained after each toss, and the total value of the dice.               [3 marks]

6a.       Write note on the factors of evaluating a model.                                                   [6 marks]

 6c. Define any five (5) common models. [10 marks] 7a. 7b. Differentiate between Physical and Mathematical Models. What is a Statistical Distribution? [10 marks] [3 marks] 7c. Enumerate seven (7) Application areas of Monte Carlo Met

6b.       Discuss how Congruential generator Algorithm generates random numbers. [4 marks]

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