Re: can a normal rv be the sum of two non-normal irvs?

   ArtflDodgr ([EMAIL PROTECTED]) wrote:

> In article <[EMAIL PROTECTED]>,
>  [EMAIL PROTECTED] (Alexander R. Pruss) wrote:
> 
> > Subject says it all: Is it possible that A+B is a normal random
> > variable when A and B are independent but not both normal (I am not
> > assuming identical distribution)?
> 
> No.  By a theorem conjectured by P. Levy and proved by H. Cramer, if the 
> sum X+Y of independent random variables has the normal distribution, 
> then so do X and Y.  A proof can be found in Cramer's book "The Elements 
> of Probability Theory".


    It's also in William Feller's celebrated two-volume
book, although I don't remember specifically where.   -- Mike Hardy