How do you pick a number randomly and uniformly from the entire set of real numbers?

The probability of x falling between 0 and 1 is the same as 10 and 11, 100 and 101, etcetera.

Never dealt with this, or if I did, I've forgotten how. Inspired by: http://answers.yahoo.com/question/index;_ylt=AiF2x...

Update:

Sorry, I want - ∞ to ∞.

Update 2:

Scythian -- Thanks. That was my thinking too, but I was hoping some of the math geniuses around here had a cute way of doing this problem.

The implications, however, are profound on Dr. D's problem. With a random and uniform distribution, you will always be dealing with infinity as part of the choosing both a and b², so the normal rules of multiplication (i.e. squaring) don't apply.

Update 3:

Thanks Scythian and (Ω)kaksi_guy. You both were helpful in filling in the gaps in my memory/skills.

2 Answers

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  • 1 decade ago
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    Remo, I don't think you're really expecting a serious answer to this one. Try this for size: Imagine a number of infinitely many digits ......x.x......., that is, including the decimal point, and every digit is picked at random from 0 to 9. What do you know? The odds are that the number picked in this way is infinite!

    Remo, I've already asked a few problems before involving this sort of thing, like, "Given 3 points at random on the plane, what's the probability that they will form an acute triangle?" And nobody can conclusively come to the "right" answer, because it all depends on how those points are chosen. There is no one "unique and correct" answer.

  • Anonymous
    1 decade ago

    there’s a standard function in MS Excel that can produce numbers 0<x<1, homogeneously spread. If you want 0<x<10, you multiply it by 10;

    -if -∞ <x <∞, then p(x) can’t be uniform, because summation of all opportunities ∫p(x)*dx must be = 1;

    -No, Dr.D’s situation has sense because there are 2 numbers to compare, not just any possible number;

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