Variance of a sum of random variables

Tuesday, 2 July 2019

3:10 PM

Variance of a sum of random variables From the properties of the covariance, it follows: Var (ax + bY) = Cov(aX + by, ax + bY) = cov(aX, ax) + cov(aX, bY) + ax) + Cov(bY, bY) = Var(aX) + Var(bY) +2 cov(aX, bY) a2Var(X) + b2Var(Y) + 2abCov(X, Y) Now, if X and Y are independent random variables, var (ax + bY) = a2Var(X) + b2Var(Y) For instance, if X and Y are independent, Var(X + Y) = Var(X) + Var( Y) var(X - Y) = Var(X) + Var(Y)

 

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