## Pseudo Random Number and Random Number

Simulation and Modeling Reference Notes

Fifth Semester | Third year

BSc.CSIT | Tribhuvan University (TU)

**Random number**

A sequence of random numbers, R_{1}, R_{2}, R_{3},…… must have two important properties;

**Uniformity**, i.e; they are equally probable everywhere.**Independence**, i.e; the current value of a random variables has no relation with the previous values.

Each random number R_{i} is an independent sample drawn from a continuous uniform distribution between zero and one. Random numbers are a necessary basic ingredient in the simulation of almost all discrete systems. Most computer languages have a subroutine, object, or function that will generate a random number. Similarly simulation languages generate random numbers that are used to generate event limes and other random variables.

For example: An electrical pulse generator can be made to drive a counter cycling from 0 to 9 and using an electronic noise generator or radioactive source the pulse can be generated as random numbers.

**Pseudo random number**

Pseudo means false, so false random numbers are being generated. The goal of any generation scheme is to produce a sequence of numbers between zero and 1 which simulates, or imitates, the ideal properties of uniform distribution and independence as closely as possible. When generating pseudo-random numbers, certain problems or errors can occur.

**Some examples of errors includes the following**

- The generated numbers may not be uniformly distributed.
- The generated numbers may be discrete -valued instead continuous valued.
- The mean of the generated numbers may be too high or too low.
- The variance of the generated numbers may be too high or low.
- There may be dependence. The following are examples:
- (a) Auto correlation between numbers.
- (b) Numbers successively higher or lower than adjacent numbers.
- (c) Several numbers above the mean followed by several numbers below the mean.