Simulation and Modeling208010 marksNumerical: random number autocorrelation testTests for Randomness - Uniformity and independence
What are the two main properties of random numbers? Test whether the 3rd, 7th, 11th, and so on numbers in the sequence in the following random number sample are auto-correlated. (Zalpha=0.05 and Z0.025=1.96) 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.
What are the two main properties of random numbers? Test whether the 3rd, 7th, 11th, and so on numbers in the sequence in the following random number sample are auto-correlated. ($Z_{\alpha}=0.05$ and $Z_{0.025}=1.96$)
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, [10]
- Uniformity: The random numbers $Ri$ are uniformly distributed on $[0,1]$. Each value is an independent draw from a continuous uniform distribution with pdf $$f(x)=\begin{cases}1 & 0\le x\le 1\ 0 & \text{otherwise}\end{cases}$$ giving $E(R)=\tfrac12$ and $Var(R)=\tfrac{1}{12}$. 2. Independence...