We have heard of several numbers in our life time—rational, algebraic, complex, real, random numbers and so on. All these have their own identity and purpose. Though we have used these numbers for various purposes, the ones that we often refer to in our analytical space are the Random Numbers.
When the term Random numbers is mentioned, immediately our attention is drawn towards extracting a sample from a lot using some random procedure. The term random is often used in the field of statistics when we face uncertainties on a general population of study. So there arises a tendency in drawing a sample of information and generalizing that to the population. But little do we know about the full potential of random numbers. How many of us are aware that Random Numbers need to possess certain properties? What are they? Why are those properties essential and where are they applied? Also, if random numbers do not have particular pattern, what is the use of generating them?
There are several important applications of Random Numbers. The interesting part of these numbers is that it could be generated to one’s desired expectation. For example, the life time of tube lights has a Gaussian property. We come to this conclusion after we record the life time of sample of bulbs and identify its properties. Also, assume that this property corresponds to some known theoretical distribution. As you know, once someone zeroed on the known distribution, then several useful information can be derived from the existing system. So it is here that random numbers play an important role. You wonder, where? Instead of collecting the sample data, we can use random numbers to generate the sample data for our desired purpose. But this is achieved based on the understanding of the existing system. For example, if I know in advance that the life time of glowing bulbs have normal property, then I use random numbers to generate the life time of 1000 bulbs having normal property. These random numbers are called normally distributed random variables. So, we could generate random numbers possessing specific properties that would be identical to our system of study. Likewise, one could generate Poisson variables, Exponential variables, Erlang Variables, Gamma Variables or any other discrete or continuous variables.
This process of getting the results of an experiment from random number generator is called simulation. In simulation we would draw inferences without actually performing the experiment. Simulation can be used to verify analytic solutions. Such an experimental study is also referred to as the Monte Carlo Method.
Monte Carlo Method seems to have come into existence in 1940, when a paper, “The Monte Carlo Method” was published by John Von Newman and Stanislav Ulam. The technique ‘Monte Carlo’ derives its name from the city of Monte Carlo in the principality of Monaco, France, famous for gambling and casinos. Gambling is the game of probability and random sampling and so is the Monto Carlo Method.
As I mentioned above, the two important statistical properties of Random Numbers are independence and Uniformity. There are several statistical tests available in order to validate these properties. So what has been written above is just a drop in the ocean of Random Numbers as there are indeed numerous applications of Random Numbers in varied fields of science.