What is central limit theorem?

What is central limit theorem?

Approach: State theorem for i.i.d. case.

For i.i.d. random variables X_i with mean μ and variance σ², sample mean Ȳ_n = (1/n)∑X_i satisfies √n(Ȳ_n - μ) → N(0,σ²) in distribution as n→∞.

Follow-up: What about non-i.i.d. cases?

Key concepts: convergence in distribution, sample mean, normal approximation.