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Fat Tails and Heavy-Tailed Distributions
Fat Tails and Heavy-Tailed Distributions
3 questions
Difficulty 4-6
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Intermediate
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counterexample
Which scenario would violate the assumptions of the Central Limit Theorem?
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A.
Averaging 10 samples from a uniform distribution, because the sample size is too small for the CLT approximation to be useful in practice
B.
Averaging samples from a Cauchy distribution, which has no finite variance, so the normalized sample mean does not converge to a Gaussian but stays Cauchy
C.
Averaging samples from a discrete Bernoulli distribution, because the CLT only applies to continuous random variables with a smooth density function
D.
Averaging samples from a highly skewed exponential distribution, because the CLT requires the underlying distribution to be approximately symmetric
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