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Let x1, . . . , xk be n-vectors, and α1, . . . , αk...

Let x1, . . . , xk be n-vectors, and α1, . . . , αk be numbers, and consider the linear combination z = α1x1 + · · · + αkxk.

Suppose the vectors are uncorrelated, which means that for i not equal to j, xi and xj are uncorrelated. Show that std(z) = sqrt(α12 std(x1)2 + · · · + αk2 std(xk)2).

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