Central Limit Theorem

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Insight:

• basically: sum of large number of independent RV has a distribution of approximately normal
• The Central Limit Theorem
  • $X_1,X_2,\cdots ,$ are sequence of independent + identically distributed RV, each have mean $\mu$, var ${\sigma }^2$ The distribution of $\frac{X_1+\cdots +X_n-n\mu }{\sigma \sqrt{n}}$ tends to the standard normal, as $n\to \infty$