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Central Limit Theorem
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Main Concept
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A sample distribution Y derived from distribution  is a distribution created by taking, for the value of Y, the average value of a sample of  instances of the variable  .
The Central Limit Theorem states that any sample distribution approaches a normal distribution as the size of the sample increases.
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A discrete distribution X is shown. Increase the sample size and notice that as the size increases, the resulting sample distribution Y (blue bars) approaches the normal distribution (red curve) which has the same mean and standard deviation as Y.
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