- CLT proof: using Taylor expansion
- only one realization( X1, X2, … Xn:a random sample of size n)
- standardized sample average (of n iid RVs) converge to standard normal distribution. or standardized sample sum converge to standard normal.
- $$Z ~ N(\mu,\sigma^2)$$, then $$Z^2 ~ chi(1)$$, by CLT, sum of n iid Z^2 follows Normal; while by defn, sum of n iid Z^2 follows chi(n).So we conclude that chi(n) converge to normal as n goes to infinity.
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