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What is wrong with the following statement of the central limit theorem? Central Limit Theorem.  If the...

What is wrong with the following statement of the central limit theorem?

Central Limit Theorem.  If the random variables X1, X2, X3, …, Xn are a random sample of size n from any distribution with finite mean μ and variance σ2, then the distribution of will be approximately normal, with a standard deviation of σ / √n.

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Answer #1

Central limit theorem :

If the random variables X1,X2, .....Xn are a random sample of size n from any distribution with finite mean and variance , then the distribution of SAMPLE MEAN, will be approximately normal with standard deviation of

the statement in the given question , the term sample mean is missing

Distribution of sample mean follow Normal with mean =

and standard deviation ,

when n is large

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