Q:
Which of the following is a provision of the central limit theorem? (Points : 1)
A skewed distribution will remain skewed however it is plotted.
There are limits to the range of

scores that can be fitted to a distribution.
A distribution based on sample means will be normal.
There will always be theoretical differences between distributions

A: In probability theory, the central limit theorem (CLT) states that, given certain conditions, the mean of a sufficiently large number of independent random variables, each with a well-defined mean and well-defined variance, [ will be approximately normally distributed. The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In

variants, convergence of the mean to the normal distribution also occurs for non-identical distributions, given that they comply with certain conditions.
In more general probability theory, a central limit theorem is any of a set of weak-convergence theories. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x| 1 where 0 < ? < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of ? as the number of variables grows. ]

cmmyg|Points 107|

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Asked 10/13/2013 3:04:21 AM

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