Standard Deviation Problem

jinydu · 2004-01-09, 09:53

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)?

Wacky · 2004-01-09, 10:36

This sounds more like a homework problem than a puzzle.

xilman · 2004-01-09, 15:57

Quote:

Originally posted by Wacky
This sounds more like a homework problem than a puzzle.

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 uniform 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

Uncwilly · 2004-01-09, 16:09

Brute force says:
0.289

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

nfortino · 2004-01-09, 23:52

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

jinydu · 2004-01-10, 02:12

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

2004-01-09, 09:53	#1
jinydu Dec 2003 Hopefully Near M48 2·3·293 Posts	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)?

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2004-01-09, 10:36	#2
Wacky Jun 2003 The Texas Hill Country 3²×11² Posts	This sounds more like a homework problem than a puzzle.

2004-01-09, 16:09	#4
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 3·7·17·31 Posts	Brute force says: 0.289 But this is not exact, rather a swipe at the answer.

2004-01-09, 23:52	#5
nfortino Nov 2003 3·5·11 Posts	I get 1/(2sqrt(3)) which is consistent with Uncwilly's approximation.

2004-01-10, 02:12	#6
jinydu Dec 2003 Hopefully Near M48 11011011110₂ Posts	That's correct, the answer is sqrt(1/12)