概率论与数理统计的题目,设随机变量X~N(2,1),Y₁,Y₂,Y₃,Y₄?
X~N(2,1),Y₁,Y₂,Y₃,Y₄均服从N(0,4),则(x-2)~N(0,1),(1/4)*∑Yi~N(0,1),所以(x-2)²服从自由度为1的x²分布,(1/16)*∑Yi²服从自由度为一的x²分布,所以Z服从F(1,1)分布,11,概率论与数理统计的题目,
设随机变量X~N(2,1),Y₁,Y₂,Y₃,Y₄均服从N(0,4)且X,Yi(i=1,2,3,4)相互独立,令随机变量Z=(16(X-2)²)/∑Yi²,试求Z的分布.
绛旓細P{X鈮3}=F(3)=(3-0)/(5-0)=3/5
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