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normal distribution

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normal distribution

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A curve used in statistics to represent the distribution of data which is symmetrical about its mean value.

In statistics, a distribution widely used to model variation in a set of data which is symmetrical about its mean value. It can be expressed in the form:

where f(x) is the relative frequency of data value x, ςis the standard deviation, μ is the mean, exp is the exponential function, and π is a mathematical constant. The curve resulting when f(x) is plotted against x is called the normal distribution curve.

An example of normal distribution can be found in the intelligence quotients (IQs) found in human populations, distributed around a mean value of 100. The distribution is also known as the Gaussian distribution after German mathematician Karl Gauss.



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The following several combination modes are used for simulation analysis, respectively: 1) Case 1: Both measurement error and parameters error obey normal distribution with zero mean and different variances; 2) Case 2: Measurement error obeys uniform distribution of zero mean, parameters error obeys normal distribution of zero mean; 3) Case 3: Measurement error obeys normal distribution of zero mean; parameters error obeys uniform distribution of zero mean.
Appendices include a random number table, the standard Normal distribution and critical values of several statistical distributions.
Humans would most likely live in an average bubble" only if A) the distribution of bubbles under consideration resembles a normal distribution (such that near-average examples are more likely than far from average ones) and B) the sample of studied universes is randomly selected and large enough to be statistically representative.
 
 
 
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