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Covariance Matrix

  1. Sep 11, 2013 #1
    if X= (3, 5, 7) & Y = (2, 4, 1)

    What is the 3x3 covariance matrix for X & Y?
     
  2. jcsd
  3. Sep 11, 2013 #2

    mathman

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    You have two variables, so the matrix is 2x2. The elements are var(X), var(Y) along the diagonal and cov(X,Y) off diagonal (both).
     
  4. Sep 11, 2013 #3
    Since 2x2 we need two diagonal elements and two off diagonal elements.

    Are the following two elements "off diagonal elements"?

    cov(X,Y) & cov(Y,X);
     
    Last edited: Sep 11, 2013
  5. Sep 11, 2013 #4

    chiro

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    Yes they are the off diagonal elements.
     
  6. Sep 12, 2013 #5
    The covariance between two jointly distributed real-valued random variables x and y with finite second moments is defined as-
    1. cov(x,y)=E[(x-E[x])(y-E[y])]

    The covariance between two jointly distributed real-valued random vectors x and y (with m and n dimensional respectively) with finite second moments is defined as
    2. cov(x,y)=E[(x-E[x])(y-E[y])T]

    What is the difference between #1 & #2?
     
    Last edited: Sep 12, 2013
  7. Sep 12, 2013 #6

    mathman

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    In this context what do you mean by dimensional? X and Y are real valued. Do you mean the number of samples?
     
  8. Sep 13, 2013 #7
  9. Sep 13, 2013 #8

    mathman

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    1 refers to real valued (1 dimensional) random variables.
    2 is a generalization to vectors (n or m dimensional) which have random variables as components.
     
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