### Author Topic: Central limit theorem and Normal distribution  (Read 310 times)

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#### palestis

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##### Central limit theorem and Normal distribution
« on: February 07, 2018, 03:50:44 AM »
That says all Mike.
And I didn't make it up. Open to everyone's interpretation.
In probability theory, the central limit theorem (CLT) establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.   (like roulette spins).
The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.    (like roulette).

For example, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, ( like past spins) .
and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to a normal distribution. A simple example of this is that if one flips a coin many times the probability of getting a given number of heads in a series of flips will approach a normal curve, with mean equal to half the total number of flips in each series.
« Last Edit: February 07, 2018, 03:57:41 AM by palestis »

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#### Mike

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##### Re: Central limit theorem and Normal distribution
« Reply #1 on: February 07, 2018, 12:14:03 PM »
palestis,

Not sure what your point is. Could you explain?

#### palestis

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##### Re: Central limit theorem and Normal distribution
« Reply #2 on: February 07, 2018, 06:31:19 PM »
It means that past spins. independent or not have a lot to do with the ultimate result.
You just have to find a way to prorate them for the short run.

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#### Reyth

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##### Re: Central limit theorem and Normal distribution
« Reply #3 on: February 07, 2018, 07:35:42 PM »
...and survive the medium runs...

Like Scep says, no bet is 100% ever and even though we may be looking at a sliver, we will encounter that sliver from time to time.

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#### scepticus

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##### Re: Central limit theorem and Normal distribution
« Reply #4 on: February 07, 2018, 08:43:45 PM »
I should have added Reyth - No bet except the deluded AP who claim to do what no one else can do !