Assignment/Tutorial 3 Computer Simulation and Modeling

Computer Simulation and Modeling

Assignment/Tutorial 3 Computer Simulation and Modeling

1. Test the following random numbers for independence by run test. Take α=0.5 and critical value Z0.025 =1.96.                                        { 37, 59, 63, 07, 92, 48, 12, 86 }
2. The sequence of numbers 0.54, 0.73, 0.98, 0.11 and 0.68 has been generated. Use the Kolmogorov-Smirnov test with α=0.05 to learn whether the hypothesis that the numbers are uniformly distributed on the interval [0,1] can be rejected. Use D0.05, 5 = 0.565.
3. What are the methods used to generate random numbers? State the properties of random numbers.
4. Consider the following sequences of random numbers. How would you test it for independence?

0.12     0.01     0.23     0.28     0.89     0.31     0.64     0.28     0.33     0.93    

0.39     0.15     0.33     0.35     0.91     0.41     0.60     0.25     0.55     0.88