Perimeter Variance of Uniform Random Triangles

Details Perimeter Variance of Uniform Random Triangles Perimeter Variance of Uniform Random Triangles

2010-07-01

arxiv.org/abs/1007.0261v1

Mathematics

Probability

9 pages

Scientific paper

Let T be a random triangle in a disk D of radius R (meaning that vertices are
independent and uniform in D). We determine the bivariate density for two
arbitrary sides a,b of T. In particular, we compute that E(a*b)=(0.837...)*R^2,
which implies that Var(perimeter)=(0.649...)*R^2. No closed-form expression for
either coefficient is known. The Catalan numbers also arise here.

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