Exact solution to std dev question

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tarahill

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The standard deviation of the following sequence +1,-1,+1,...+1,-1 is 1.
If each term is multiplied by a random number between 0 and 1, the expected standard deviation of the sequence appears to be about 0.5788...
Can anyone tell me the exact number and whether there is an elegant calculation or formula that gives rise to it?
 
tarahill said:
The standard deviation of the following sequence +1,-1,+1,...+1,-1 is 1.
If each term is multiplied by a random number between 0 and 1, the expected standard deviation of the sequence appears to be about 0.5788...
Can anyone tell me the exact number and whether there is an elegant calculation or formula that gives rise to it?
Click to expand...
The result of your procedure is a uniform random distribution of numbers between -1 and +1. the standard deviation of a uniform distribution is the full width divided by sqrt(12).
 
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