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If a bunch of random variables are independently and identically distributed with an exponential distribution, their sum apparently follows a Gamma distribution.
But according to the central limit theorem, for with mean zero and variance , becomes normally distributed as n gets sufficiently large, regardless of the distribution of .
Doesn't this imply that the sum becomes approximately normally distributed, ?
So, what's the deal with the distribution of a sum of i.i.d. exponentials? Does the sum of i.i.d. exponential random variables follow a Gamma distribution, but the sum of samples drawn randomly from an exponential distribution converge to a normal distribution? I don't understand the distinction. What's going on here? Thorstein90 ( talk) 00:09, 17 December 2012 (UTC)
Look at the Rotunda (geometry) article. Because the pentagonal rotunda is the only one made entirely out of regular polygons, this question might be tough. But I want to know if anyone can add an image of a hexagonal rotunda (for which having non-regular polygons as lateral faces is a must) to the article?? Georgia guy ( talk) 01:40, 17 December 2012 (UTC)
BTW, shouldn't the plural form of rotunda be rotundae? :-) Double sharp ( talk) 09:45, 20 December 2012 (UTC)
I am familiar with the theory of dynamical chaos, but am interested in slightly different problems.
Suppose a n-dimensional set of dynamical equations is known to exhibit chaotic dynamics, I am interested in the related systems:
where is stochastic noise, and is observed directly.
and , but only can be observed and is again stochastic noise.
I would be appreciative of any useful suggested reading that I could do to learn more about such cases. Particularly regarding how to distinguish the two cases, and hoe the dynamical chaos is still evident given the introduction of noise.
Many thanks. — Preceding unsigned comment added by 123.136.64.14 ( talk) 03:23, 17 December 2012 (UTC)
Mathematics desk | ||
---|---|---|
< December 16 | << Nov | December | Jan >> | December 18 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
If a bunch of random variables are independently and identically distributed with an exponential distribution, their sum apparently follows a Gamma distribution.
But according to the central limit theorem, for with mean zero and variance , becomes normally distributed as n gets sufficiently large, regardless of the distribution of .
Doesn't this imply that the sum becomes approximately normally distributed, ?
So, what's the deal with the distribution of a sum of i.i.d. exponentials? Does the sum of i.i.d. exponential random variables follow a Gamma distribution, but the sum of samples drawn randomly from an exponential distribution converge to a normal distribution? I don't understand the distinction. What's going on here? Thorstein90 ( talk) 00:09, 17 December 2012 (UTC)
Look at the Rotunda (geometry) article. Because the pentagonal rotunda is the only one made entirely out of regular polygons, this question might be tough. But I want to know if anyone can add an image of a hexagonal rotunda (for which having non-regular polygons as lateral faces is a must) to the article?? Georgia guy ( talk) 01:40, 17 December 2012 (UTC)
BTW, shouldn't the plural form of rotunda be rotundae? :-) Double sharp ( talk) 09:45, 20 December 2012 (UTC)
I am familiar with the theory of dynamical chaos, but am interested in slightly different problems.
Suppose a n-dimensional set of dynamical equations is known to exhibit chaotic dynamics, I am interested in the related systems:
where is stochastic noise, and is observed directly.
and , but only can be observed and is again stochastic noise.
I would be appreciative of any useful suggested reading that I could do to learn more about such cases. Particularly regarding how to distinguish the two cases, and hoe the dynamical chaos is still evident given the introduction of noise.
Many thanks. — Preceding unsigned comment added by 123.136.64.14 ( talk) 03:23, 17 December 2012 (UTC)