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The Normal (or Gaussian) distribution is a member of the exponential family of probability distributions. It is symmetrical function whose shape is determined by two parameters: the mean and variance (or standard deviation). The distribution s additive so that if two variables, X and Y are normally distributed then, even if their means and variances are different, their sum (and difference) are normally distributed with parameters that are simply related to the separate ones.
It is not an easy distribution to calculate and so it has been necessary to tabulate key values.
According to the law of large numbers, if you take repeated independent samples from any distribution, the means of those samples are distributed approximately normally. The greater the size of each sample, or the greater the number of samples, the more closely the results will match the normal distribution. This characteristic makes the Normal distribution central to statistical theory.
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What is normal distribution in statstics?
The normal distribution is a statistical distribution. Many naturally occurring variables follow the normal distribution: examples are peoples' height, weights. The sum of independent, identically distributed variables - whatever their own underlying distribution - will tend towards the normal distribution as the number in the sum increases. This means that the mean of repeated measures of ANY variable will approach the normal distribution. Furthermore, some distributions that are not normal to start with, can be converted to normality through simple transformations of the variable. These characteristics make the normal distribution very important in statistics. See attached link for more.
What is the difference of a normal distribution and a stardard normal distribution?
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
Is the normal distribution infinite?
The domain of the normal distribution is infinite.
What does a negative kurtosis mean?
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
Are all unimodal distributions normal?
No. Normal distribution is a special case of distribution.
