Proof (Variance of the sum or difference of the two random variables.) var(x+y)=v(x)+v(y)+2cov(x,y)

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Pillai_"Var(X+Y): Variance of the Sum of Two Random Variables"

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 difference of random variables: Var(X-Y) = Var(X)+Var(Y)-2Cov(X,Y)

Covariance and Correlation in Probability

Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) Proof

Variance of sum and difference of random variables | Random variables | AP Statistics | Khan Academy

Covariance result V[X + Y] = V[X] + V[Y] + 2 Cov(X, Y)

Expected Value and Variance of Discrete Random Variables