Random Number and Pseudo Random Number | BSc.CSIT | Fifth Semester 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, R1, R2, R3,…… must have two important properties;

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

Each random number Ri 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

1. The generated numbers may not be uniformly distributed.
2. The generated numbers may be discrete -valued instead continuous valued.
3. The mean of the generated numbers may be too high or too low.
4. The variance of the generated numbers may be too high or low.
5. 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.
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