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Consider the following sequence of random numbers 0.15, 0.94, 0.05, 0.51 and 0.29 has been generated. Use Kolmogorov-Smirnov test to determine whether the hypothesis of uniformity can be rejected

given α=0.05 and Critical value D=0.565).

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Step 1)$ H_0: R_i~$ Uniformly (0, 1)

$H_1: R_i~$ is not Uniformly (0, 1)

Step 2) Number of random numbers= N= 5

Step 3) Arrange all random numbers in ascending order

         0.05, 0.15, 0.29, 0.51, 0.94

Step 4)

I i/N $R_i$ $i/N-R_i$ i-1 (i-1)/N $R_i$-((i-1)/N)
1 0.2 0.05 0.15 0 0 0.05
2 0.4 0.15 0.25 1 0.2 -0.05
3 0.6 0.29 0.31 2 0.4 -0.11
4 0.8 0.51 0.29 3 0.6 -0.09
5 1.0 0.94 0.06 4 0.8 0.14

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It means that the given samples have property of uniformity.

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