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Covariance of a set of uniformly distributed unit vectors?

I have a set of uniformly distributed unit vectors within a "cone" (essentially a subset of a uniform distribution on the unit sphere, as described here). I've found how to get the covariance matrix ...
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1answer
328 views

What is cov(X,Y), where X=min(U,V) and Y=max(U,V) for independent uniform(0,1) variables U and V?

Let $X=\min(U,V)$ and $Y=\max(U,V)$ for independent uniform(0,1) variables $U$ and $V$. What's the covariance of $X$ and $Y$? Could you develop some calculations, especially regarding the computation ...
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1answer
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Covariance matrix of uniform spherical distribution

I need to figure out the covariance matrix of a uniform spherical distribution. But there I can't even find a closed form of the distribution. This link says it is $\frac{1}{n}\mathbf{I}$, where ...