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/
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