Wendel'S Theorem

(Theory)

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What is Wendel's theorem?

In geometric probability theory, Wendel's theorem, named after James G. Wendel, gives the probability that N points distributed uniformly at random on an -dimensional hypersphere all lie on the same "half" of the hypersphere. In other words, one seeks the probability that there is some half-space with the origin on its boundary that contains all N points. Wendel's theorem says that the probability is The statement is equivalent to being the probability that the origin is not contained in the convex hull of the N points and holds for any probability distribution on Rn that is symmetric around the origin. In particular this includes all distribution which are rotationally invariant around the origin.

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probability theorempropositionstatementtheoremtheorems in geometrytheory

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