Standard Deviation Problem
 

Suppose I randomly choose n real numbers between 0 and 1. As n approaches infinity, the mean of all the random numbers will obviously approach 0.5.

But what number will the standard deviation approach (exactly)?

This sounds more like a homework problem than a puzzle.

[QUOTE][i]Originally posted by Wacky [/i]
[B]This sounds more like a homework problem than a puzzle. [/B][/QUOTE]
And a poorly phrased one, too.

What is the probability distribution from which the samples are drawn? I don't see that we can conclude from the question as stated that the samples must be drawn from the [b]uniform[/b] distribution. All we are told are the bounds on their values. The "obvious" observation about the mean, which is far from obvious to me, restricts the distribution function somewhat, but not enough for an unambiguous value to be placed on the standard deviation.


Paul

Brute force says:
[spoiler]0.289[/spoiler]

But this is not exact, rather a swipe at the answer.

I get [spoiler]1/(2sqrt(3))[/spoiler] which is consistent with Uncwilly's approximation.

That's correct, the answer is sqrt(1/12)