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- University
- Politecnico di Milano
- Degree programme
- Mathematical Engineering
- Subject
- ProbabilitÃ
- Material language
- Italian
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- Exercises · By topic
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ExercisesBy topicItalian
1 Esercizi su sufficienza 2C 20minimalit C3 A0 20e completezza
Study material for ProbabilitÃ, shared by the Studwiz community and reviewed by moderators.
ProbabilitÃBy topic
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M/O.small/D.small/E.small/L.small/L.small/I.small /E.small M/E.small/T.small/O.small/D.small/I.small /D.small/E.small/L.small/L.small’I/N.small/F.small/E.small/R.small/E.small/N.small/Z.small/A.small S/T.small/A.small/T.small/I.small/S.small/T.small/I.small/C.small/A.small A.A. 2019/2020 Esercizi 1 Esercizio 1. Sia X1/comma.math/period.math/period.math/period.math/comma.mathX/n.mathun campione estratto dalla popolazione avente densit` a /f.math(/x.math) = e/theta.alt−/x.math1[/theta.alt/comma.math+∞)(/x.math)/comma.math /theta.alt >0 determinare una statisticaT sufficiente e minimale per/theta.alt, mostrare che T ` e anche completa. Esercizio 2. Sia X1/comma.math/period.math/period.math/period.math/comma.mathX/n.mathun campione estratto dalla popolazione avente densit` a /f.math(/x.math) = 2/theta.alt/x.mathe−/theta.alt/x.math2 1(0/comma.math+∞)(/x.math)/comma.math /theta.alt >0 determinare una statisticaT sufficiente e completa per/theta.alt, T ` e anche minimale? Mostrare che S =X non ` e sufficiente. Esercizio 3. Sia X1/comma.math/period.math/period.math/period.math/comma.mathX/n.mathun campione estratto dalla popolazioneX∼ Beta(/a.math/comma.math/b.math), (/a.math>0/comma.math/b.math>0). x Se /a.math` e incognito e/b.mathnoto, determinare una statistica sufficiente e completa per/a.math; y se /b.math` e incognito e/a.mathnoto, determinare una statistica sufficiente e completa per/b.math; z se /a.mathe /b.mathsono entrambi incogniti, determinare una statistica sufficiente e completa per (/a.math/comma.math/b.math). Esercizio 4. Sia X1/comma.math/period.math/period.math/period.math/comma.mathX/n.mathun campione estratto dalla popolazione X∼ Beta(/theta.alt/comma.math/theta.alt), (/theta.alt >0). Deter- minare una statistica sufficiente e completa per/theta.alt. Esercizio 5. Sia…
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