Discovering Statistics

A den for Learning

RANDOM NUMBER GENERATORS

What are random numbers?

Imagine yourself picking up a card from a well shuffled full deck of cards. What could the card you picked be? The jack of spades, the king of diamonds, or the queen of hearts?? Well it could be the ace of clubs too or it could be any of the other available cards in the deck.

In terms of probability theory, you can definitely say that picking up a card from a well shuffled full deck of cards is a ‘random experiment’. It is an experiment because, when one picks up a card there is an outcome, a result of the effort. And a random one cause you definitely know all the possible cards that may be picked.

Also in this particular random experiment of picking a card from a well shuffled full deck of cards, no card is preferred over the other. In simple words, the probability of picking up any card is the same, in statistical sense, the event of picking a particular card and the event of picking up another card will be equally likely. This is what we call a random phenomenon. So, picking up a card from a well shuffled full deck of cards could be interpreted as picking a card randomly from a full deck of cards.

Now imagine yourself selecting a number from the set (0,1,2,3,4,5,6,7,8,9) randomly. It means that you selecting 0 or 1 or 2 or 3 or …. or 9 are equally likely events. Thus, we are selecting a random number from the set.

How to generate random numbers?

A random number from the set of numbers can be generated by using the following methods:

• Lottery Method: Suppose there are n numbers in the set. One can then take n similar balls such that each ball is given a unique number from the set, and put it in an urn. Shuffle the balls , and then start picking up the balls one by one with replacement and note down the number on each of the balls picked. The numbers noted will be the random numbers.
• Roullette Wheel: One can also take a roulette wheel and divide the wheel into n equal pieces and writing the numbers(uniquely from the set) on each of the areas and spin the wheel, and note down the number. Here too the numbers noted will be random numbers.
• Random Number Table: The above two methods are physical and it always take a considerate amount of time to draw random numbers that way. So instead, one can use a random number table, a table where random numbers are stacked up. However, since the random numbers drawn by one may be duplicated by another quite easily, there has always been an uncertainty about randomness in this method, we quite oftenly call the random numbers drawn by this method to be pseudo- random numbers.

Drawing Random Numbers using algorithms (for computers)

Since a computer is a deterministic device, it might seem impossible that it could be used to generate random numbers. The numbers generated are algorithmically computed and are quite deterministic. However, they appear to be random and must pass stringent tests designed to ensure that they can provide the same results that truly random numbers (such as the first two methods above) would be produced.

Requirements of a Random Number Generator:

1. It should be fast.
2. It should be repeatable.
3. It should be amenable to analysis.
4. It should have a long period.
5. It should be apparently random.

Some Random Number Generator (RNF) Methods