QUESTION (20 MARKS)
(a) Given the following set of random numbers 0.50,0.64,0.65,0.41,0.86,0.23,0.61,0.89,0.11,0.24. Determine if these numbers are uniformly distributed using Kolmogoror Smirnor test at = 0.05. (6 Marks) (b) A sequence of 10,000 five digit random numbers has been generated and an analysis of numbers indicate that there are 3075 numbers having five different digits, 4935 having a pair, 1135 having two pairs, 695 having three of a kind, 105 having a full house (three of a kind and a pair) 54 having four of a kind and one having all five of a kind. Use Poker test to determine if these random numbers are independent at = 0.01. (6 Marks) (c) A dentist schedules all her patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending upon the type of dental work to be done as summarized below. Category Time required in minute frequency Filling 45 25 Crowning 60 15 Cleaning 15 25 Extracting 45 10 Check up 15 25
Simulate the dentists clinic for about four hours and determine the average waiting time for the patients and the percentage idle time for the dentist. Assume all the patients show up at the clinic at exactly their scheduled arrival time starting at 8.00am. use the following random number 40, 82, 11, 34, 52, 66, 17, 70. (8 Marks)
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QUESTION (20 MARKS)
(a) Discuss the techniques 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) Use the linear congruential method to generate five random numbers given that 0 = 1, = 3, = 7 = 15. (5 Marks) (d) Briefly discuss the areas where simulation is applicable. (4 Marks)
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