Central Limit Theorem
Statement
Equivalently:
where is the standard normal CDF.
Convergence in Distribution
Berry-Esseen Theorem
This gives a rate of convergence for the CLT.
Applications
Practical Rule
CLT for Sums
Continuity Correction
When approximating a discrete distribution with the normal:
Delta Method
Multivariate CLT
Lindeberg-Feller CLT
Examples
Example 1: Sum of fair dice:
Example 2: Number of heads in coin flips:
Example 3: Sample mean of exponential() with :