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Math Help - Simple question on variance

  1. #1
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    Simple question on variance

    Let X and Y be random variables with mean E(x)= u(1) = 1, E(y)=u(2) = 4, and variance, var(x) = 4, var(y) = 6 , and roe, p = 1/2.
    Find the mean and the variance of Z = 3x -2y. The answers are -5 and 30.6


    How did they get this? I know that
    var(z) = var(3x) + var(-2y) +2Cov(xy)

    I am not getting the right answer out for variance, and I don't really have any idea on finding the mean. Can someone break it down to me? Thanks.
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  2. #2
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    Quote Originally Posted by Dream View Post
    Let X and Y be random variables with mean E(x)= u(1) = 1, E(y)=u(2) = 4, and variance, var(x) = 4, var(y) = 6 , and roe, p = 1/2.
    Find the mean and the variance of Z = 3x -2y. The answers are -5 and 30.6


    How did they get this? I know that
    var(z) = var(3x) + var(-2y) +2Cov(xy)

    I am not getting the right answer out for variance, and I don't really have any idea on finding the mean. Can someone break it down to me? Thanks.
    Things you're expected to know and use: If Z = aX + bY then:


    E(Z) = a E(X) + b E(Y)


    Var(Z) = a^2 Var(X) + b^2 Var(Y) + 2ab Cov(X, Y)


    \rho = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} \Rightarrow Cov(X, Y) = \rho \, \sigma_X \, \sigma_Y
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