Abstract
In the present paper a formula for calculation of the density function \(f_{\rho}(x)\) of the distance between two independent points randomly and uniformly chosen in a bounded convex body \(D\) is given. The formula permits to find an explicit form of density function \(f_{\rho}(x)\) for body with known chord length distributions. In particular, we obtain an explicit expression for \(f_{\rho}(x)\) in the case of a ball of diameter \(d\).
A simulation model is suggested to calculate empirically the cumulative distribution function of the distance between two points in a body from \(R^{n}\), where explicit form of the function is hard to obtain. In particular, simulation is performed for balls and ellipsoids in \(R^{n}\).
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The research of the first author was supported by RA MES State committee of Science (grant no. 18T-1A252).
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Aharonyan, N.G., Khalatyan, V. Distribution of the Distance Between Two Random Points in a Body from \(\boldsymbol{R}^{\boldsymbol{n}}\) . J. Contemp. Mathemat. Anal. 55, 329–334 (2020). https://doi.org/10.3103/S1068362320060023
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DOI: https://doi.org/10.3103/S1068362320060023