My friend and I have a bet going about the definition of the Central Limit Theorem.
If we define an example as a number drawn at random from some probability density function where the function has a defined finite mean and variance. And we define a sample as a set of size N examples (with N>1).
Then, we take S samples and create a sampling distribution D over the means of each individual sample.
I am arguing that the Central Limit Theorem states that as the number of samples S approaches infinity, then the sampling distribution D will approximate a normal distribution.
My friend is arguing that the Central Limit Theorem states that given any number of samples S, sampling distribution D will not necessarily approximate a normal distribution, but as the number of examples per sample N approaches infinity, then D will approximate a normal distribution.
Who is right?
Update: I lost this bet.