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I have some trouble understanding the concept of a covariance matrix. For instance, I'm going over this question that says: assume that we have U1, U2 and U3 as independent zero-mean, unit-variance Gaussian random variables. Furthermore, we have X = U1, Y = U1 + U2, and Z = U1 + U2 + U3. We're asked to find the covariance matrix for (X,Y,Z).

I just require some guidance/hints on how to solve this sort of a problem. And I'd really appreciate any help on this matter.

Stanly
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    Let's start by focusing your question: is your trouble over understanding how to arrange the three covariances into a matrix or is it in understanding covariance or is it in computing covariances of such (linear) combinations of Normal variables? – whuber Nov 10 '14 at 01:05
  • @whuber I believe it's a combination of the first and the third one. :( – Stanly Nov 10 '14 at 01:16
  • I have done some searching. The most effective keywords were ["covariance linear combination"](http://stats.stackexchange.com/search?q=covariance+linear+combination). The answer at http://stats.stackexchange.com/a/38722, found with that search, directly and thoroughly addresses the third issue. I don't believe anyone has asked about the first issue. Please, then, edit your question to focus on the issue of arranging covariances into a matrix. When you do so, add the [tag:self-study] tag. – whuber Nov 10 '14 at 01:27
  • Ah... an answer to the first issue can be found at http://stats.stackexchange.com/a/56235 (the result of searching for ["covariance matrix"](http://stats.stackexchange.com/search?q=covariance+matrix). It looks, then, like every aspect of your question already has an answer somewhere on our site :-). Is that the case or is there something that still needs to be addressed? – whuber Nov 10 '14 at 01:31
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    @whuber Thank you so much! That's exactly what I was looking for. :) – Stanly Nov 10 '14 at 01:39

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