## A Sum of Gaussian Random Variables is a Gaussian Random Variable

A basic result from the theory of random variables is that when you*sum*two independent random variables, you

*convolve*their probability density functions (PDF). (Equivalently, in the frequency domain, their

*characteristic functions multiply*.)

That the sum of two independent Gaussian random variables is Gaussian follows immediately from the fact that Gaussians are closed under multiplication (or convolution).

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