Question

27.2 Generate 15 numbers using a seed of x0 = 1 in the following generator: xn = (5xn-1 + 1) mod16.

Perform a K-S test and check whether the sequence passes the test at a 95% confidence level.

Answer 1

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AS FOR GIVEN DATA..

Generate 15 numbers using a seed of x0 = 1 in the following generator: xn = (5xn-1 + 1) mod16.

Perform a K-S test and check whether the sequence passes the test at a 95% confidence level.

EXPLANATION :-

Rcode:

> options(scipen = 999)
> x<-vector()
> x[1]=1;
> for(i in 2:15){
+ x[i]=((5*x[i-1])+1)
+ x[i]=x[i]%%16
+ }
> ks.test(x,"pnorm")

   One-sample Kolmogorov-Smirnov test

data: x
D = 0.91058, p-value = 0.0000000000000006661
alternative hypothesis: two-sided

a)

1 6 15 12 13 2 11 8 9 14 7 4 5 10 3

b)

From the p-value obtain from K-S test, this can be said that the sample follows normal distribution.

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