Random Numbers and Random Number Generators

Question 1	What is a Random Number resp What is a Random Number Generator.
Question 2	What are examples of sequences of Random Numbers and which are not.
Question 3	What is the best way to test if a sequence of numbers can be called a sequence of Random numbers
Question 4	Is it possible to generate a random numbers by means of a computer program ?

Purpose

For a critical evaluation of a document which uses RND's and PRND's (pseudo RND's) study this: Feeling the Future: Experimental Evidence for Anomalous Retroactive Influences on Cognition and Affect

Answer question 1

A Random Number is a number generated by a process which generates random numbers. This is called a random number generator.
A random number generator always generates numbers between two ranges. As such you can have:

• a sequence a random numbers between 0 and 1. For example 011001110101001101010
• a sequence of random numbers between 0 and 9. For example 25945718340328
• a sequence of random numbers of of each 5 digits. etc For example 12897 54376 54892 36004

The definition of a random number generator is:

A random number generator is a process which creates number between a certain range in such a way that each next number is completely independent of the previous way.
This translates in the following rule: The chance of finding any value should be equal.
Or: The correlation between any two numbers should be 0 (No correlation)

Answer question 2

• Is the following sequence of 20 numbers random ?: 00000000000000000000
  The chance of finding 20 zero numbers in a row is 2^-20. This number is very small and the sequence is non random.
• Is the following sequence of two numbers of each 3 bits random ?: 000 000
  The chance of finding two equal numbers one after an other is 2^-8. This is high. In fact this sequence is too small to decide if it is generated by a true random process.
• Does the Visual Basic function RND generate true random numbers ? No. The RND function is cyclic. After 2^24 calls it generates the same number.

Answer question 3

The best way to test if a process generates random numbers is described in the NIST article: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications Special Publication 800-22 Revision 1a
This document describes 15 tests in order to declare a sequence as random or not random.

Answer question 4

1. The first process is an ON OFF process. This program calculates each 15.6 millisecond an increase or decrease in process value in combination with the Visual Basic RND function. The direction is decided by a dead band. In its free time the RND function is continuous called in combination with performing other functions on the PC. This makes the outcome of the program unpredictable or random. It takes one second to calculate one bit.
2. The second process is must faster. Each 15.6 ms a bit is calculated in combination with the RND function and by performing the other tasks on the PC.

Reflection

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