數(shù)理統(tǒng)計(jì)教程課后重要答案解析習(xí)題

1、完美WD格式專業(yè)整理知識(shí)分享第一章第一章:統(tǒng)計(jì)量及其分布統(tǒng)計(jì)量及其分布19.設(shè)母體服從正態(tài)分布N和分別為子樣均值和子樣方差又設(shè)???2???2nS且與獨(dú)立試求統(tǒng)計(jì)量的抽樣分布.??21~???Nn?n???21?111????nnSnn??解:因?yàn)榉姆植?所以????1n???????210?nnN而??10~121Nnnn????????1~222?nnSn??且與獨(dú)立所以分布.2nS????1n??1~1111???????ntS

2、nnnnSnnn???即服從分布.111????nnSnn????1?nt20.是取自二元正態(tài)分布N的子樣設(shè)??1niii???????????222121和????????????niiininiinSnn1211111???????2??2121????niinS???試求統(tǒng)計(jì)量的分布.???????????????????niiniiiniir12211??????????122221??????nSrSSS????????解:由

3、于??.21???????E.???????????????cov2DDDnnnn2122212???????所以服從分布.????n212221212????????????????10N????????????????211212121222122?????????????????????????????????iiniiiniiniiniSrSSSn完美WD格式專業(yè)整理知識(shí)分享由于故是極大似然估計(jì).??01ln222???????

4、?nL?????niiLxn1ln1???(2)由令得211?????E?????211.112???????14.設(shè)為取自參數(shù)為的普哇松分布的一個(gè)子樣.試證子樣平均和n??1???都是的無(wú)偏估計(jì).并且對(duì)任一值??????niinnS122)(11???10??????21nS?????也是的無(wú)偏估計(jì).?證:對(duì)普哇松分布有從而?????DE.???E??.11212?????????????????DEnESinin故與都是的無(wú)偏估計(jì).

5、又?2nS?????????????????????112nSE故也是的無(wú)偏估計(jì).??21nS??????15.設(shè)為取自正態(tài)母體的一個(gè)子樣試適當(dāng)選擇使1n?????2??Nc為的無(wú)偏估計(jì).??21112??????niiicS??2?解:由且相互獨(dú)立可知???iE2???iDn??1?從而2????????jijiEEEji???????????212112211212122??????EnEncEEEEcESiiiini???????