#math #stats #econ 

[statistics - Adding and Subtracting Normal Distributions - Mathematics Stack Exchange](https://math.stackexchange.com/a/1072571/874090)
More generally, if X1,…,Xn are independent normal random variables with means μi and variances σ2i, and c1,…,cn are constants, Y=c1X1+…+cnXn is normal with mean μY=c1μ1+…+cnμn and variance c21σ21+…+c2nσ2n. Here you're doing the case n=3 with c1=−1,c2=1,c3=1.
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