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I'm working my assignment and it's a really odd assignment to me. For:-

  1. Show $\Sigma$ given by (1) is qualified as a covariance matrix. I don't know if there is a qualification criteria for a covariance matrix?
  2. Find distribution of $(x_1, x_3)$; Is there any theorem for the distribution of a row in a normal distributed data?
  3. distribution of $x_{12}$.Is there any theorem for the distribution of a point in a normal distributed data?

Could anyone give me some hints or related materials? Thanks : )

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1 Answer 1

up vote 2 down vote accepted
  1. $\Sigma$ should be positive semidefinite and symmetric to be a covariance matrix.

  2. The distribution of the rows would be a multivariate normal with covariance matrix given by $\Sigma$ with the second row and column deleted.

  3. The point $x_{12}$ would have the distribution taken by $\textbf{x}_2$, since this is the distribution it is drawn from.

Hope that helps.

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As always, Wikipedia has more en.wikipedia.org/wiki/Covariance_matrix –  Simon Hayward Oct 29 '12 at 11:44
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Thanks for your help. Hope you be better next year! –  J.A.F Oct 29 '12 at 12:10
    
Cheers! Getting better at the stats now, still find the programming difficult, but getting lots of help on Stack Overflow :D –  Simon Hayward Oct 29 '12 at 12:15
    
It's good to hear that! By the way,what's programming language are you learning? R? –  J.A.F Oct 29 '12 at 12:45
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let us continue this discussion in chat –  J.A.F Oct 29 '12 at 13:07
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