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Math Help - 3 Gaussian random variables, independence

  1. #1
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    3 Gaussian random variables, independence

    Hi!

    Let's suppose we have 3 independent Gaussian random variables with means m_x, m_y, m_z (they can be different) and variances sigma^2 (the same for all):

    X ~ N(m_x, sigma^2)
    Y ~ N(m_y, sigma^2)
    Z ~ N(m_z, sigma^2)

    The question: are (X - Y) and (X - Z) independent? How can I proove it?

    Thanks!

    Kornel
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  2. #2
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    Quote Originally Posted by cornail View Post
    Hi!

    Let's suppose we have 3 independent Gaussian random variables with means m_x, m_y, m_z (they can be different) and variances sigma^2 (the same for all):

    X ~ N(m_x, sigma^2)
    Y ~ N(m_y, sigma^2)
    Z ~ N(m_z, sigma^2)

    The question: are (X - Y) and (X - Z) independent? How can I proove it?

    Thanks!

    Kornel
    The covariance is not zero, so they are not independent.
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