Idea

There are no "truly random" numbers in our deterministic world (at least in classical physic). Nevertheless, we need random numbers for many statistical methods, like Monte Carlo Simulation.

How we can get the random numbers, that are the White Noise?

Random numbers that a computer generates appear random but are produced by a deterministic algorithm (Strictly speaking, we therefore talk about "pseudo-random" numbers)

Properties

Good random number generator:

• has a long period (produces many distinct values before repeating)
• allows to reproduce any random sequence
• is fast
• is portable across computing platforms
• produces the output, that appears statistically random

Simplest Random Numbers Generator

Linear Congruential Random Numer Generator:

Given: $x_0$ (seed), $a, c, m$

Formula: $x_i = (a * x_{i-1} + c) \mod m$ , $i ≥ 1$