Associated Topics || Dr. Math Home || Search Dr. Math

Functions of Random Numbers

```
Date: 08/26/98 at 16:59:26
From: Reg Reid
Subject: Random numbers

I don't know where to start thinking about this. If you add or multiply
one random number by a non-random number, do you still get a random
number? It seems that you would, but I can't prove it.
```

```
Date: 08/27/98 at 12:40:02
From: Doctor Peterson
Subject: Re: Random numbers

Hi, Reg.

The answer depends partly on what you mean by random number. I assume
you are thinking of an evenly distributed random number, that is, one
that is equally likely to have any value within its range. But are you
thinking of an integer, or a "real" number? And what do you think of as
its range? That will make some difference.

Suppose you roll a die (a random number from 1 to 6) and then add 3 to
it. Then you are equally likely to get any number from 4 to 10. So the
result is random in that sense. But if you multiply it by 3 instead,
you are equally likely to get any of 3, 6, 9, 12, 15, or 18. Some
numbers between 3 and 18 will be missed, so although it is randomly
distributed over those six values, it is not random in some senses.

If you are thinking of random numbers as generated by a computer,
whether this makes a difference depends on what you are doing with the
number. If you are generating random numbers in some range by getting
a random number and then doubling it, the resulting numbers would be
random enough for some purposes; but if you use them to sample some
numbers and determine what percentage of them are even, you would think
that all numbers are even! And if you used them to select math problems
from a list to ask someone, you would find that you never asked the
odd-numbered questions.

On the other hand, your random number may be given to you as a real
number between 0 and 1. If you double it, you will get a random number
between 0 and 2. What I've just described will still happen, but it
will be hidden deep in the last digits of a decimal, and for most
purposes you could ignore it.

So my answer is that the result is still "random," but only if you are
aware of the restrictions you have made on the values the random
number can have, and don't do anything that will be affected by it.

Does that help?

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search