# Problem 1 - How do we show that the output is Gaussian?

From MurrayWiki

**Q:** How do we show that the output is Gaussian?

**A:** After showing the pdf for y is as given in the problem statement, you only need to show that the mean and variance of y are the sum of the mean and variance of the two random variables x1 and x2. You do not need to show that all of the higher-order moments for y are 0 (as is the case with Gaussian variables) because this was not discussed in the lectures.

--John