If 
and 
are independent variates and 
is a normal distribution,
then both 
and 
must have normal distributions. This was proved
by Cramér in 1936.
Cramér's Theorem
See also
Normal DistributionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Cramér's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CramersTheorem.html