Journal of Jishou University(Natural Sciences Edition) ›› 2021, Vol. 42 ›› Issue (3): 1-5.DOI: 10.13438/j.cnki.jdzk.2021.03.001

• Mathematics •     Next Articles

Proof That  n-Dimensional Normally Distributed Linear Functions Obey Normal Distribution

XING Jiasheng, YANG Yichuan,WU Sang   

  1. (1. School of Mathematics and System Science, Beihang University, Beijing 100191, China;2. LMIB of the Ministry of Education, Beihang University, Beijing 100191, China)
  • Online:2021-05-25 Published:2021-08-29

Abstract: A method is given to prove that the n-dimensional normally distributed linear functions obey normal distribution. First,  the n-dimensional normally distributed linear function is expressed as the linear function of the n-dimensional standard normal distribution by the transitivity of linear transformation. Then, the linear function of n-dimensional normal distribution is proved to obey normal distribution by using the property that the linear functions of mutually independent normal distribution obey normal distribution.

Key words: n-dimensional normal distribution, n-dimensional standard normal distribution, linear transformation, linear function

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