Chapter 3 - Random Numbers

Computer Simulation and Modeling

Chapter 3 - Random Numbers 

Important Questions from Chapter 3 - Random Numbers

 

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

5. Explain Convolution method.

6. Write a note on “Acceptance – Rejection Technique”

7. Records pertaining to the monthly number of job-related injuries at an underground coal mine were being studied by a federal agency. The values for the past 100 months were as follows: Injuries per month Frequency of occurance 0 35 1 40 2 13 3 6 4 4 5 1 6 1 Apply Chi-Square test to test these data to test the hypothesis that the underlying distribution is Poisson. (use a level of significance α = 0.05 ,        = 5.99).

8. Explain inverse transform techniques.