I'm trying to find the standard deviation of the following distribution: $Z = kX + vY$ where $k$ and $v$ are scalar values, therefore it isn't a normal sum but it is the sum of two weighted normally distributions.
Thanks in advance!
Standard deviation of the sum of two normally distributed random variables with a weight [duplicate]
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$\begingroup$ It doesn't matter what distributions $X$ and $Y$ have: the SD is the square root of the variance, so you only need to compute the variance. See stats.stackexchange.com/search?q=linear+combination+variance for many answers. $\endgroup$– whuber ♦Commented May 8, 2021 at 14:47
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$\begingroup$ @whuber, would my resulting variance equal to $σ^2 (z) = k*σ^2 (x) + v*σ^2 (y)$ then? $\endgroup$– NoplattsCommented May 8, 2021 at 15:23
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$\begingroup$ No, that can't be right, because when both $k$ and $v$ are negative you would get a negative value, which is impossible. Plug your values into the formula given in the answer to the first duplicate at stats.stackexchange.com/a/191588/919. $\endgroup$– whuber ♦Commented May 8, 2021 at 16:29
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