试题与答案

设总体X~N(0,σ2),X1,…,X10是取自X的简单随机样本,令,统计量服从F(

题型:填空题

题目:

设总体X~N(0,σ2),X1,…,X10是取自X的简单随机样本,令

,统计量

服从F(m,n)分布,则a=______.

答案:

参考答案:

解析:

[分析]: 由于正态总体的样本均值[*]与样本方差S2相互独立,并且[*]-
[*],所以有
[*]
由于[*]相互独立,根据F分布的性质,有
[*]
因此[*]

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