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Math Help - Obtain Cov(X,Y+Z)

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    Obtain Cov(X,Y+Z)

    For random variable X,Y and Z ,
    it is given that Cov(X,Y) = a and Cov(X,Z)=c
    Obtain Cov(X,Y+Z).
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    Hello,
    Quote Originally Posted by Stats View Post
    For random variable X,Y and Z ,
    it is given that Cov(X,Y) = a and Cov(X,Z)=c
    Obtain Cov(X,Y+Z).
    The covariance is a bilinear and symmetric form.

    So Cov(X,Y+Z)=Cov(X,Y)+Cov(X,Z)

    Many of the properties of covariance can be extracted elegantly by observing that it satisfies similar properties to those of an inner product:

    (1) bilinear: for constants a and b and random variables X, Y, and U, Cov(aX + bY, U) = a Cov(X, U) + b Cov(Y, U)
    (2) symmetric: Cov(X, Y) = Cov(Y, X)
    (3) positive semi-definite: Var(X) = Cov(X, X) ≥ 0, and Cov(X, X) = 0 implies that X is a constant random variable (K).
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