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 Distribution## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Cramér's Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/CramersTheorem.html