Variance of the sum of independent random variables in spheres

Q2 Mathematics
J. Lacalle, L.M. Pozo Coronado
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引用次数: 1

Abstract

The sum of random variables (errors) is the key element both for its statistical study and for the estimation and control of errors in many scientific and technical applications. In this paper we analyze the sum of independent random variables (independent errors) in spheres. This type of errors are very important, for example, in quantum computing. We prove that, given two independent isotropic random variables in an sphere, X1 and X2, the variance verifies V(X1+X2)=V(X1)+V(X2)V(X1)V(X2)2 and we conjecture that this formula is also true for non-isotropic random variables.

球体中独立随机变量和的方差
随机变量(误差)的和是其统计研究以及在许多科学和技术应用中误差估计和控制的关键因素。本文分析了球面上独立随机变量(独立误差)的和。这种类型的错误非常重要,例如,在量子计算中。我们证明了,给定球面上的两个独立的各向同性随机变量X1和X2,方差验证了V(X1+X2)=V(X1)+V(X2) - V(X1)V(X2)2,并推测该公式对非各向同性随机变量也成立。
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来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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