Simulation and modeling - Old Questions

5.  What do you mean by Pseudo random numbers?

Pseudo random numbers are the random numbers that are generated by using some known methods (algorithms) so as to produce a sequence of numbers in [0,1] that can simulates the ideal properties of random numbers. They are not completely random as the set of random numbers can be replicated because of use of some known method.

Every new number is generated from the previous ones by an algorithm. This means that the new value is fully determined by the previous ones. But, depending on the algorithm, they often have properties making them very suitable for simulations.

When generating pseudo-random numbers, certain problems or errors can occur. Some examples include the following:

1. The generated numbers might not be uniformly distributed.
2. The generated numbers might be discrete valued instead of continuous valued.
3. The mean of the generated numbers might be too high or too low.
4. The variance of the generated numbers might be too high or too low.
5. There might be presence of correlation between the generated numbers.

The important considerations that should be made while generating pseudo random numbers are as follows:

1. The method used to generate random number should be fast because the simulation problem requires a large set of random numbers which can increase time complexity of the system.
2. The method used should be portable to different platform and programming languages so as to generate same results wherever it is executed.
3. The method should have long cycle.
4. The random numbers should be replicable. It means that the same set of random numbers should be generated with same starting point.
5. The generated random numbers should approximate the uniformity and independence properties.