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设X～N（μ σ2) X1 X2 … X10是X的样本试求下列概率：

大学 2020-12-22 22:14:14 样本,概率已帮助人

设X～N(μ，σ²)，X₁，X₂，…，X₁₀是X的样本，试求下列概率：

热搜：一个式子是x的三阶无穷小

答案解析

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由于X～N(μ，σ2)，所以
Xi～N(μ,σ2),i=1,2,..,10
$latex.action?latex=XGZyYWN7WF97aX0tzrx9e8%2BDfe%2B9nk4oMCwxKQ%3D%3D$
$latex.action?latex=XGxlZnQoIFxmcmFje1hfe2l9Lc68fXvPg30gXHJpZ2h0KV57Mn3vvZ7Ph157Mn0oMSk%3D$ , $latex.action?latex=XHN1bV97aT0xfV57MTB9XGxlZnQoIFxmcmFje1hfe2l9Lc68fXvPg30gXHJpZ2h0KV57Mn3vvZ7P%0D%0Ah157Mn0oMTAp$
因而
$latex.action?latex=UFxsZWZ0KDAuMjbPg157Mn3iiaRcZnJhY3sxfXsxMH1cc3VtX3tpPTF9XnsxMH0oWF97aX0tzrwp%0D%0AXnsyfeKJpDIuM8%2BDXnsyfVxyaWdodCk%3D$
$latex.action?latex=PVBcbGVmdCgyLjbiiaRcc3VtX3tpPTF9XnsxMH1cbGVmdChcZnJhY3t4X3tpfS3OvH17z4N9XHJp%0D%0AZ2h0KV57Mn3iiaQyM1xyaWdodCk%3D$
=P(χ2(10)﹥2.6)-P(X2(10)﹥23)
=0.99-0.01=0.98$由X～N(μ，σ2)得
$latex.action?latex=XGZyYWN7XHN1bV97aT0xfV57MTB9KFhfe2l9LVxvdmVybGluZXtYfSleezJ9fXvPg157Mn19772e%0D%0Az4deezJ9KDkp$
所以
$latex.action?latex=UFxsZWZ0KDAuMjbPg157Mn3iiaRcZnJhY3sxfXsxMH1cc3VtX3tpPTF9XnsxMH0oWF97aX0tXG92%0D%0AZXJsaW5le1h9KV57Mn3iiaQyLjPPg157Mn1ccmlnaHQp$
$latex.action?latex=PVBcbGVmdCgyLjbiiaRcc3VtX3tpPTF9XnsxMH1cbGVmdChcZnJhY3tYX3tpfS1cb3ZlcmxpbmV7%0D%0AWH19e8%2BDfVxyaWdodCleezJ94omkMjNccmlnaHQp$
=P(χ2(9)﹥2.6)-P(χ2(9)﹥23)=0.975-0.005=0.97