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

In article <[EMAIL PROTECTED]>,
Alexander R. Pruss <[EMAIL PROTECTED]> 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)?

This is the Levy-Cramer Theorem.  The answer is no.

The easiest proof is to use the moment generating function,
which is exp(Q(t)), where Q(t) = m*t + v*t^2/2, v the
variance.  It then follows that the moment generating
functions of A and B exist for all complex values, and are
hence are non-zero entire functions.  This makes their
logarithms entire, and it then follow that those functions
are bounded by quadratics, and hence are quadratics.


-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
[EMAIL PROTECTED]         Phone: (765)494-6054   FAX: (765)494-0558