NATIONAL OPEN UNIVERSITY OF NIGERIA

UNIVERSITY VILLAGE, PLOT 91, CASDASTRAL ZONE, NNAMDI AZIKIWE EXPRESS WAY, JABI, ABUJA.
FACULTY OF SCIENCES
MAY/JUNE 2012 EXAMINATION

COURSE CODE:                    CIT 412    
COURSE TITLE:                    Modelling and Simulation
TIME ALLOWED:                    3 Hours
INSTRUCTIONS:                    Answer any Five (5) Questions in all

Q1.a    Enumerate six (6) properties of a good Random number generator.              [6 marks] 
      b.     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

       c.    State four types of Simulations                                  [4 marks]
      d.    Highlight the advantage of using Model                              [3 marks]

Q2.a    Briefly explain what is meant by a Model.                              [5 marks] 
      b.    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] 
      c.     Explain Queuing theory.                                      [5 marks]

                            
Q3.a    What is a Random Number?                                  [3 marks] 
      b.     State the Theorem of Multiplication of Probabilities.                      [9 marks] 
      c.     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]

Q4.a    Discuss Poisson Process.                                      [6 marks] 
      b.     Why simulation language?                                             [10 marks] 
      c.     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]

Q5.a    Discuss Monte Carlo algorithm and highlight the methods used by the algorithm.      [7 marks] 
      b.     Explain in detail the queuing disciplines and its four (4) methods/disciplines.             [10 marks] 
      c.     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]

Q6.a    Write note on the factors of evaluating a model.                          [6 marks]
      b.     Discuss how Congruential generator Algorithm generates random numbers.          [4 marks]  
      c.     Define any five (5) common models.                                    [10 marks]

Q7.a    Differentiate between Physical and Mathematical Models                         [10 marks]
      b.    What is a Statistical Distribution?                                  [3 marks]
      c.    Enumerate seven (7) Application areas of Monte Carlo Met                  [7 marks]