Central Limit Theorem Statement---Liapounoff

• This extended theorem reads:

• If are independent random variables with possibly different distributions, and:

  

• where must exist (not necessary in Laplace's version where all had same distribution).

• Let

  

• Then if ,

• then y is Gaussianly distributed with

  mean and

  standard deviation .

• Note the does when exists in Laplace's case as and .