Wald’s Identity vs. Tail Sum Formula

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-03-13 DOI:10.1080/00029890.2023.2184165

Reza Farhadian, V. Ponomarenko

引用次数: 0

Abstract

n=1 P(N ≥ n). Here the first equality is justified because ∑N n=1 Xn = ∑∞ n=1 XnI{N ≥ n}; the second because the Xi’s are nonnegative; the third because N is independent of the Xi’s; and the last because the Xi’s are identically distributed. —Submitted by Reza Farhadian, Razi University and Vadim Ponomarenko, San Diego State University doi.org/10.XXXX/amer.math.monthly.122.XX.XXX MSC: Primary 60C99

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Wald恒等式与尾和公式

n=1P（n≥n）。这里第一个等式是合理的，因为∑N=1Xn=∑∞N=1XnI{N≥N}；二是因为Xi是非负的；三是因为N独立于Xi；最后一个原因是Xi是同分布的-Reza Farhadian，拉兹大学和Vadim Ponomarenko提交，圣地亚哥州立大学doi.org/10.XXX/amer.math.monthly.122.XX.XXX MSC:Primary 60C99

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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