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How to weight two normally distributed random variables to minimize the variance of their sum
Posted on 2011-03-05
I have 2 normally distributed random variables, A and B, with variances a^2 and b^2, respectively, and I calculate the weighted sum of A and B as: C = (1-k)A + kB, where k is a constant, 0<k<1.
What value of k will minimize the variance of C?