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Why Sums of Independent Gaussians Are Always Gaussian — The One-Line Proof
Moment generating function. MGF of Gaussian distribution. Completing the square. Normal distribution proof. Sum of independent Gaussians. Mean and variance from MGF. Probability density function. Convex function exponential. Closed form MGF. Why are sums of independent Gaussians always Gaussian? The answer is hiding in one definition: the ...
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