Why does Var(x+a)=Var(x), Var(x-a)=Var(x), Var(X ± a) = Var(X) : var(x+a)=var(x) proof

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Extending Var(X) to Var(X ± a) and Var(aX) : ExamSolutionsExtending Var(X) to Var(X ± a) and Var(aX) : ExamSolutions
Proof for the variance of a sum of random variables: Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)Proof for the variance of a sum of random variables: Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)
Why does Var(a)=0, Var(X ± a) = Var(X) and Var(aX) = a²Var(X) : ExamSolutionsWhy does Var(a)=0, Var(X ± a) = Var(X) and Var(aX) = a²Var(X) : ExamSolutions
Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) ProofVar(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) Proof
Proof for the variance of a difference of random variables: Var(X-Y) = Var(X)+Var(Y)-2Cov(X,Y)Proof for the variance of a difference of random variables: Var(X-Y) = Var(X)+Var(Y)-2Cov(X,Y)
Discrete Random Variables The Expected Value of X and VarXDiscrete Random Variables The Expected Value of X and VarX
Proof that variance of a constant times X is the constant squared times var of X: Var(aX)=a^2 Var(X)Proof that variance of a constant times X is the constant squared times var of X: Var(aX)=a^2 Var(X)
C7) Prove that Var(X-Y)=Var(X)+Var(Y)-2Cov(X,Y)C7) Prove that Var(X-Y)=Var(X)+Var(Y)-2Cov(X,Y)