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Cisy 403:Simulation And Modelling Question Paper

Cisy 403:Simulation And Modelling

Course:Computer Science

Institution: Kenya Methodist University question papers

Exam Year:2013

KENYA METHODIST UNIVERSITY

END OF 1ST TRIMESTER 2013 (EVENING) EXAMINATION

FACULTY : COMPUTING & INFORMATICS
DEPARTMENT : CIS & BI
UNIT CODE : BBIT 417/CISY 403
UNIT TITLE : SIMULATION AND MODELLING
TIME : 2 HOURS

Instructions: Answer Question ONE and any other TWO Questions.

Question One

(a) Using a multiplicative congruential generator defined by Z=27, a = 8, c = 27 and m= 100. Generate a sequence of 5 random numbers. (5 Marks)

(b) A random variable X how the following empirical distribution.

X 1 3 4 6 8 10
P (X) 0.10 0.20 0.25 0.20 0.15 0.10

Plot the CDF and find the values of X corresponding to the following two-digit random numbers, 05, 45, 62, 93. (5 Marks)

(c) Customers arrive at a watch repair shop according to a poisson process at a rate of one per every 10 minutes and the service time is an exponential random variable with mean 8 minutes.

Find;
(i) Average number of customers in the system. (2 Marks)
(ii) Average time a customer spends in the shop. (2 Marks)
(iii) Average time a customer spends in waiting for the services.
(3 Marks)
Suppose the arrival rate of the customers increases by 10 percent. Find the corresponding changes in the above measures (i), (ii) and (iii). (5 Marks)

(d) Differentiate between the following:

(i) Physical and mathematical model. (2 Marks)
(ii) Station and dynamic model. (2 Marks)

(e) Explain how inverse transform method can be used to generate random numbers from:

(i) Binomial distribution. (2 Marks)
(ii) Poisson distribution. (2 Marks)

Question Two

(a) Discuss the congruential method as a generator used to generate random numbers. (6 Marks)
(b) What are the advantages of using simulation other than experimenting with real life systems? (5 Marks)
(c) Highlight possible limitations of using simulation techniques. (4 Marks)
(d) Discuss the techniques used to generate random numbers. (5 Marks)

Question Three

(a) Briefly discuss areas where simulation is applicable. (5 Marks)
(b) Explain how a set of random numbers can be generated from the following functions.
(i) f(x) = 3x2 (2 Marks)
(ii) f(x) = (1 Mark)

(c) What are the standard capabilities and differences in all simulation languages. (8 Marks)
(d) Differentiate between simulation language and simulators. (4 Marks)

Question Four

(a) State the properties of a good estimator. (4 Marks)

(b) A company is considering the problem of marketing a new product. The investment required in the project is 2 million Kenya shillings. There are two factors that are uncertain annual demand and profit. The management has the past data regarding the possible levels of the two factors.

Annual Demand
Probability
Profit
Probability

1,000
2,000
3,000
4,000
5,000 0.10
0.20
0.40
0.20
0.10 3.00
5.00
7.00
9.00
10.00 0.10
0.20
0.40
0.20
010

Given the following set of random numbers for demand and profit.
Demand: 35, 55, 10, 30, 70, 90, 25, 52, 62, 31.
Profit: 15, 80, 50, 90, 30, 60, 25, 62, 10, 2.
Use monte-Carlo simulation to determine the following:
(i) Average Profit
(ii) Average demand
(iii) Return of investment (given by)
(10 Marks)
Simulated demand x Simulated Profit X 1,000,000
2,000,000

(c) Briefly explain the properties of the following;

(i) Poisson distribution (2 Marks)
(ii) Binomial distribution (2 Marks)
(iii) Normal distribution (2 Marks)

Cisy 403:Simulation And Modelling Question Paper

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