# Random Number Generation

Random numbers are used in many places. The occurrence of sounds in nature, run time of buses between the same stops, travel time between home and office everyday, variable expenditure every month, predicting the face of a coin when tossed up, predicting the sum on two faces of a dice when cast. All of these phenomenon have a certain degree of randomness.

Random numbers are numbers generated in sequence which do cannot be predicted. For example if the equation of a variable is Y = 5 * X + 4 X can be completely predicted from Y. Random numbers occur between 0 and 1 and are perfectly normally distributed. For example when generated in large numbers random numbers occur equally between 0 and 1 along the Gaussian curve. That is between 0 and 0.1 there would be the same amount of numbers as between 0.8 and 0.9. Random numbers are required in simulation studies for example simulation of driving time between two destinations, simulation of a pair of dice, simulation of a. There are many different kinds of random number generators the most important is the linear congruential generator.

These numbers when generated have to satisfy many defined statistical tests for periodicity, normality etc., However the numbers generated by many generators are pseudo random. It is very important to use perfect random numbers to analyze discrete event systems using simulation models so that we get replications of the simulation models that are statistically independent. These are also generated using sounds in nature and other naturally occurring phenomenon.

Random variates can also be generated using such numbers. These random variate can be uniform, Poisson, normal etc., In this case one would require to generate the cumulative distribution function For example a quantity such as “time of waking up in the morning ” can vary between 5:30 AM to 9:00 AM. In case there is an equal probability of waking up anytime between 5:30 AM and 9:00 AM then the time of waking up can be given as Time of waking up = 5:30 + r * 210 where r is a number that varies between 0 and 1.

Now, if one notices in the equation above if r is generated uniformly between 0 and 1 the time of waking up would vary uniformly between 5:30 and 9:30. But the distribution of r is not normal then one could find more values of r generated between 0.4 and 0.5 than say 0.9 and 1. So when the act of waking up is simulated one would find more data values between 6:54 and 7:15 AM yielding a wrong inference or a false conclusion to the simulation model. It is hence very important to use a generator that yields normally distributed data.