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the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)

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Distribution of random vectors

Two positive numbers $\alpha$ and $\beta$ are given. We are going to describe a process of choosing a random vector on the unit sphere $S$ in $\mathbb R^3$ (given by $x^2+y^2+z^2=1$). A vector $u\in …