The central limit theorem states that the sum of N iid random variables
Central Limit Theorem
As a result of the central limit theorem, we can approximate discrete distributions as a normal distribution.
Intuition
An intuitive explanation of the central limit theorem is that sum of random variables can be viewed as a sequence of convolution operations. As convolution smooths functions, repeatedly applying convolutions eventually gives us the bell-curve shape.
Related
- law of large numbers - describes the behavior of sample mean for sum of iid random variables
References
Footnotes
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In certain continuous distributions (e.g. a t-distribution with 2 DOF), the variance can diverge into infinity ↩