Central Limit Theorem (CLT )
Theorem Let X1,X2, _,Xn be independently, identically distributed random variables with finite mean / and variance 02 Denote the sum of X is by Sn = Xi + + Xm, then
Sn np no?
N(0,1) in distribution, when n - OO
Roughly speaking, as long as the sample size n is large enough, the left random variable above can be approximated by standard normal variable very well: