Simulation and Modeling208210 marksNumerical: Autocorrelation test for randomnessTests for Randomness - Uniformity and independence
What are the properties of random numbers? The sequence of numbers 0.23, 0.45, 0.67, 0.12, 0.89, 0.34, 0.56, 0.78, 0.19, 0.41, 0.63, 0.08, 0.85, 0.29, 0.51, 0.73, 0.16, 0.94, 0.37, 0.59 has been generated. Test for the independence among numbers in the sequence starting with index i = 2 and lag m =
What are the properties of random numbers?
The sequence of numbers 0.23, 0.45, 0.67, 0.12, 0.89, 0.34, 0.56, 0.78, 0.19, 0.41, 0.63, 0.08, 0.85, 0.29, 0.51, 0.73, 0.16, 0.94, 0.37, 0.59 has been generated. Test for the independence among numbers in the sequence starting with index $i = 2$ and lag $m = 3$ using auto-correlation test. ($\alpha = 0.05$, $Z_{\alpha/2} = 1.96$)[10]
Random numbers $Ri$ must satisfy two key properties: 1. Uniformity The numbers are uniformly distributed on $(0,1)$; every value is equally likely. The pdf is: $$f(x) = \begin{cases} 1 & 0 \le x \le 1 \ 0 & \text{otherwise} \end{cases}$$ with $E(R) = \tfrac{1}{2}$ and $Var(R) = \tfrac{1}{12}$. 2...