# What's the distribution of a row in a normal distributed data?

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. $\Sigma$ 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
Thanks for your help. Hope you be better next year! – John Hass 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? – John Hass Oct 29 '12 at 12:45
– John Hass Oct 29 '12 at 13:07