Probability and Statistics (5): Law of Large Numbers and the Central Limit Theorem

Sat, 24 Aug 2024 09:00:00 +0000

If you had to choose just two theorems from all of probability theory, you’d choose these: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT). Together, they answer two fundamental questions. The LLN says: “Yes, your sample average will converge to the true mean.” The CLT says: “And here’s exactly what the fluctuations look like.” Without these theorems, there’s no justification for opinion polls, no reason to trust clinical trials, and no explanation for why stochastic gradient descent converges.

Convergence on Chen Kai Blog

Probability and Statistics (5): Law of Large Numbers and the Central Limit Theorem