2
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Why do variances add when summing independent random variables?
I think you can indeed think about it in terms of Pythagorean theorem. So the point is that you can think of random variables as vectors in some space, so the variance of a random variable is like the ...
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1
vote
Why do variances add when summing independent random variables?
The other answers explain how the additivity of variance for sums of independent random variables on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$ follows from orthogonality/Pythagoras' ...
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