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Math Help - bivariate normal distribution - how do I even do this?

  1. #1
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    Unhappy bivariate normal distribution - how do I even do this?

    The bivariate distribution: Bivariate Normal Distribution -- from Wolfram MathWorld

    The question states:

    Let X and Y have the bivariate normal (3,5,2,4,0.5) distribution.
    a)Specify the marginal distribution of X.
    b)Specify the marginal distribution of Y.

    I have no idea how to do this. Can someone help?

    From my book the only thing I could establish was
    X=3+2Z
    Y=5+4(Z/2 + C*sqrt(3/4))
    where Z and C are independent random variables, both distributed N(0,1).
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  2. #2
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    If I'm interpreting your notation properly, you can read off the marginal distributions using the parameters of the bivariate distribution. If X and Y are jointly bivariate normal, then each of X and Y is normally distributed. You simply need to specify the mean and variance for each. If I'm reading this properly, X has mean 3 and variance 2, and Y has mean 5 and variance 4. I'm guessing the 0.5 is either the covariance or correlation, but this doesn't impact the marginals.
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  3. #3
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    I'm still not sure how to properly write the marginal distribution of X and Y.

    the notation of
    (3,5,2,4,0.5)
    is
    (u1,u2,sigma1,sigma2,p)

    p is the correlation
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