Today I Learned

Some of the things I've learned every day since Oct 10, 2016

26: Partial and Pseudo-Linearity of Variance

If two random variables A, B are independent, then

\textrm{Var}(A + B) = \textrm{Var}(A) + \textrm{Var}(B).

However, this is not true in general. It is always the case, however, that for a constant scalar c,

\textrm{Var}(c A) = c^2 \textrm{Var}(A).

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