System Simulation and Modeling - IInd Internal Question Bank

SYSTEM MODELLING & SIMULATION QUESTION BANK II INTERNALS

VIII CS 10CS82

Unit-III

1. Explain the following in Discrete Distributions:

a) Bernoulli’s Distributions/Trials. (5)

b) Binomial Distributions (5).

2. Generate Three Poisson variates with mean α=0.2.Compute e-α. Generate Three Random

  Numbers and compute the results in Tabular form.

3. a) Explain Uniform Distributions in detail(5).

b) Explain Weibull Distributions in detail(5).

4. Explain Poisson process.

5. a) Explain the procedure for generating a Poisson random variate (5).

b) Explain Triangular distributions (5).

6. Explain the following Continuous Distributions:

a) Log Normal Distributions.(5)

b) Triangular Distributions.(5)

7. Explain the following Continuous Distributions:

a) Gamma Distributions.(5)

b) Erlang Distributions.(5)

8. Explain the following Continuous Distributions:

a) Uniform Distributions. (5)

b) Exponential Distributions. (5)

9. Explain Empirical Distributions.

Unit-V

1a) Explain the Properties of Random Numbers?

b) Explain the Generation of Pseudo-Random Numbers?

2. Explain Various Tests for Random Numbers?

3. The sequence of numbers 0.44,0.81,0.14,0.05,0.93 has been generated. Use kolmogorov- smirnov test with alpha=0.05 to determine if the hypothesis that its number are uniformly distributed on interval (0,1) can be rejected. First the numbers must be ranked fro smallest to largest. Compare F(x) and Sn (x) on a graph?

4. Test for whether the 3^rd,8^th 13^th and so on, numbers in the sequence at the beginning are autocorrelated using alpha=0.05.Here, i=3(beginning with the third number),m=5(every five numbers),N=30(30 numbers n the sequence),and M=4(Largest integer such that 3+(M+1)5<=30).

0.12 0.01 0.23 0.28 0.89 0.31 0.64 0.28 0.83 0.93

0.99 0.15 0.33 0.35 0.91 0.41 0.60 0.27 0.75 0.88

0.68 0.49 0.05 0.43 0.95 0.58 0.19 0.36 0.69 0.87

5. Differentiate between Chi-square and K-S Test?

6. Using χ2(Chi Square) test, Test for Hypothesis that the data given follows Uniform Distribution at alpha=0.05.The Critical value is 16.9

O(i)

8

8

10

9

12

8

10

14

10

11

7. Explain in detail the Inverse Transform technique for Exponential Distributions (10).