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Tribhuvan university CSIT 2065 Syllabus Simulation and modeling Old Questions 2070

Simulation and modeling - Old Questions

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Syllabus Notes Old Questions Unit Wise Questions Question Bank

9.  The sequence of numbers 0.54, 0.73, 0.97, 0.10 and 0.67 has been generated. Use the Kolmogorov-Smirnov test α=0.05 to determine if the hypothesis that the numbers are uniformly distributed on the interval [0, 1] can be rejected. (Note that the critical value of D for α=0.05 and μ=5 is 0.565).

5 marks
Asked in 2070

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Official Answer

Given sequence of number,

    0.54, 0.73, 0.97, 0.10 and 0.67

Arranging the given number in ascending order:

    0.10, 0.54, 0.67, 0.73, 0.97

Here, N = 5

Calculation table for Kolmogorov-Smirnov test :

i



10.100.20.10.10
20.540.4-0.34
30.670.6-0.27
40.730.80.070.13
50.9710.030.17

Now, calculating

\\begin{displaymath}D^+ = {\\rm max}_{1 \\le i \\le N} \\left\\{ \\frac{i}{N} - R_{(i)} \\right\\} \\end{displaymath} = 0.1

\\begin{displaymath}D^- = {\\rm max}_{1 \\le i \\le N} \\left\\{ R_{(i)} - \\frac{i-1}{N} \\right\\} \\end{displaymath} = 0.34

$D = {\\rm max} (D^+, D^-)$ = 0.34

Given, Critical value $D_\\alpha$ = 0.565

Since the computed value, D = 0.34, is less than the tabulated critical value, $D_\\alpha$ = 0.565, the hypothesis of no difference between the distribution of the generated numbers and the uniform distribution is not rejected.