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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 : )

1 Answers 1

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  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.

  • 1
    let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/6270/discussion-between-peng-teng-and-simon-hayward)2012-10-29