== Central Limit Theorem ==
 * [[WikiPedia:Asymptotic analysis]]
 * Central Limit Theorem (CLT):
  * sample size가 크다면 distribution of averages of iid variables (properly normalized) = a standard normal distribution
  * Normalization: ( X - ''μ'' ) / ( ''σ'' / sqrt(n) ) = Z ~ N( 0, 1 )
   * When population SD ''σ'' is unknown, the standard error of the sample mean (SEM) = SD of those sample means over all possible samples
   * SEM = SD / sqrt(n)
   * ''σ'' / sqrt ( ''n'' ) = the standard error of the sample mean
 * Suppose X_1, X_2, ... X_n are independent, identically distributed random variables from an infinite population with mean ''μ'' and variance ''σ''^2^.
  * if n is large, the mean of the X's, call it X', is approximately normal with mean ''μ'' and variance ''σ''^2^ / n.
  * 則, X'~ N( ''μ'', ''σ''^2^ / n ).

 * 예시1: 동전 던지기, 앞면 확률 P(h)= ''p'' 라면, E(h) = ''p'', variance = ''p'' ( 1 - ''p'' )
  * 동전 던지기를 n 번씩 했을 때, 그 결과의 평균값이 ''μ''이라면,
  * normalization: ( ''μ'' - ''p'' ) / SD = ( ''μ'' - ''p'' ) / sqrt ( ''p'' ( 1 - ''p'' ) / n )

==== 추가 자료 ====
 * [[http://dermabae.tistory.com/146]]