Evidence that the amount of 2 Gaussian variables is an additional Gaussian

The amount of 2 Gaussian variables is an additional Gaussian.
It appears all-natural, yet I can not locate an evidence making use of Google.

What's a brief means to confirm this?
Many thanks!

Modify: Given both variables are independent.

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2019-05-06 00:05:57
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Answers: 1

I do not recognize just how I missed out on that, without a doubt :
http://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables
Thanks Kaestur Hakarl!

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2019-05-08 15:47:39
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