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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

2
  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.

  • 0
    As always, Wikipedia has more https://en.wikipedia.org/wiki/Covariance_matrix2012-10-29
  • 1
    Thanks for your help. Hope you be better next year!2012-10-29
  • 0
    Cheers! Getting better at the stats now, still find the programming difficult, but getting lots of help on Stack Overflow :D2012-10-29
  • 0
    It's good to hear that! By the way,what's programming language are you learning? R?2012-10-29
  • 0
    R and F#, plus a number of others in my spare time (Python, JavaScript, HTML & CSS on CodeAcademy).2012-10-29
  • 0
    Wow!So many!I'm learning R and Matlab. It seems you are interested in programming.2012-10-29
  • 0
    I think that it is not possible to be an effective statistician without being able to handle A LOT of data now, and often that means getting data from lots of places, each with their own langauge specific access path.2012-10-29
  • 1
    let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/6270/discussion-between-peng-teng-and-simon-hayward)2012-10-29