Bài giảng xác suất thống kê và ứng dụng phần 8 phan thanh hồng

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Bài giảng xác suất thống kê và ứng dụng phần 8   phan thanh hồng

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❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ P❤❛♥ ỗ ổ t P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✶ ✴ ✾✶ P❤➛♥ ❱■■■ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t❤❛♠ sè ❝õ❛ ♠ët tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✷ ✴ ✾✶ P❤➛♥ ❱■■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ❜✐➳t ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ ♣❤÷ì♥❣ s❛✐ tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✸ ✴ ✾✶ P❤➛♥ ❱■■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ❜✐➳t ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ ♣❤÷ì♥❣ s❛✐ tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✸ ✴ ✾✶ P❤➛♥ ❱■■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ❜✐➳t ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ ♣❤÷ì♥❣ s❛✐ tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✸ ✴ ✾✶ P❤➛♥ ❱■■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ❜✐➳t ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ ♣❤÷ì♥❣ s❛✐ tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✸ ✴ ✾✶ P❤➛♥ ❱■■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ❜✐➳t ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ ♣❤÷ì♥❣ s❛✐ tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✸ ✴ ✾✶ P❤➛♥ ❱■■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ❜✐➳t ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❑✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ✈➲ ♣❤÷ì♥❣ s❛✐ tê♥❣ t P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✸ ✴ ✾✶ ✣➦t ❣✐↔ t❤✉②➳t ✈➲ t❤❛♠ sè tê♥❣ t❤➸ ❚❤õ tư❝ ❦✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ❧✉ỉ♥ ❜➢t ✤➛✉ ✈ỵ✐ ✈✐➺❝ ✤➦t ❣✐↔ t❤✉②➳t✱ ❣✐↔ t❤✉②➳t ❧➔ ♠ët ♣❤→t ❜✐➸✉✱ ♠ët ♥❤➟♥ ✤à♥❤✱ ♠ët ✤➲ ①✉➜t ✈➲ t❤❛♠ sè tê♥❣ t❤➸✳ ❇➔✐ t♦→♥ ❦✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ❧✉æ♥ ❝â ♠ët ❝➦♣ ❣✐↔ t❤✉②➳t ❧➔ ❣✐↔ t❤✉②➳t ❦❤æ♥❣ ❍✵ ✈➔ ❣✐↔ t❤✉②➳t ✤è✐ ❍✶ ✳ ❱✐➺❝ ❦✐➸♠ ✤à♥❤ ❞➝♥ tỵ✐ ✶ tr♦♥❣ ✷ q✉②➳t ✤à♥❤✿ ❦❤ỉ♥❣ ❜→❝ ❜ä ❍✵ ✭❧♦↕✐ ❍✶ ✮ ❤♦➦❝ ❜→❝ ❜ä ❍✵ ✭❝❤➜♣ ♥❤➟♥ P ỗ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✹ ✴ ✾✶ ✣➦t ❣✐↔ t❤✉②➳t ✈➲ t số tờ t tt ổ ỵ ❍✵ ♠ỉ t↔ ❤✐➺♥ t÷đ♥❣ ❧ó❝ ❜➻♥❤ t❤÷í♥❣✱ ♠ỉ t↔ t➻♥❤ tr↕♥❣ ♥❣✉②➯♥ t❤õ②✱ ❤♦➦❝ t➻♥❤ tr↕♥❣ ❦❤æ♥❣ ❝❤à✉ t→❝ ✤ë♥❣ ❣➻ ❝õ❛ ❤✐➺♥ t÷đ♥❣✳ ●✐↔ t❤✉②➳t ❍✵ ❦❤ỉ♥❣ ❜à ❜→❝ ❜ä trø ❦❤✐ ❝â ✤õ ❜➡♥❣ ❝❤ù♥❣ t❤è♥❣ ❦➯ ❝❤♦ t❤➜② ♥â s❛✐✳ ❑❤✐ ①➙② ❞ü♥❣ ❍✵ ✱ tr♦♥❣ ❝➜✉ tró❝ ❝õ❛ ♥â ❧✉ỉ♥ ❝â ♠ët ❞➜✉ ❜➡♥❣✱ ❝â t❤➸ ❧➔ =✱ ≤✱ ❤♦➦❝✱ ≥✳ ♣ ●✐↔ t❤✉②➳t ✤è✐✱ ỵ ổ t t tr ữủ ợ ❍✵ ✳ ●✐↔ t❤✉②➳t ❍✶ ✤÷đ❝ ❝❤➜♣ ♥❤➟♥ ❝❤➾ ❦❤✐ ❝â ✤õ ❜➡♥❣ ❝❤ù♥❣ t❤è♥❣ ❦➯ ❝❤♦ t❤➜② ♥â ✤ó♥❣✳ ❑❤✐ ①➙② ❞ü♥❣ ❍✶ ✱ tr♦♥❣ ❝➜✉ tró❝ ❝õ❛ ♥â ❦❤æ♥❣ ❝â ❞➜✉ ❜➡♥❣✱ ❝â t❤➸ ❧➔ =✱ > ❤♦➦❝ < P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✺ ✴ ✾✶ P❤➙♥ ♣❤è✐ ❝õ❛ Pˆ✶ − Pˆ✷ ●✐↔ sû t❛ ❝➛♥ s♦ s→♥❤ t✛ ❧➺ sè ♣❤➛♥ tû ❝õ❛ ❤❛✐ tê♥❣ t❤➸ ❝â t➼♥❤ ❝❤➜t ♥➔♦ ✤â ❧➔ ♣✶ ✱ ✈➔ ♣✷ ✳ ❈❤å♥ tø ♠é✐ tê♥❣ t❤➸ ♠ët ♠➝✉ ♥❣➝✉ ♥❤✐➯♥ ❝ï ♥✶ ✱ ♥✷ ✱ ❣å✐ Pˆ✶ ✈➔ Pˆ✷ ❧➔ t✛ ❧➺ ♠➝✉✳ ◆➳✉ ❤❛✐ ♠➝✉ ✤÷đ❝ ❝❤å♥ ♠ët ❝→❝❤ ✤ë❝ ❧➟♣ t❤➻ ♣❤➙♥ ♣❤è✐ ❝õ❛ Pˆ✶ − Pˆ✷ ♥✶ ✱ ♥✷ ❧ỵ♥ ✭♥✶ ♣✶ ✱♥✶ (✶ − ♣✶ )✱ ♥✷ ♣✷ ♥✷ (✶ − ♣✷ ) ➼t ♥❤➜t ❜➡♥❣ ✺✮ ✶ ❳➜♣ ①➾ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ♥➳✉ ✷ ❈â tr✉♥❣ ❜➻♥❤ µ ˆ ˆ = P✶ −P✷ ✸ ❈â ✤ë ❧➺❝❤ ❝❤✉➞♥ ♣✶ P P = P ỗ ▲❖◆●✮ ♣✶ (✶ − ♣✶ ) ♣✷ (✶ − ♣✷ ) + ♥✶ ♥✷ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✼✾ ✴ ✾✶ ❑✣●❚ ❝❤♦ sü ❦❤→❝ ❜✐➺t ❝õ❛ ❤❛✐ t✛ ❧➺ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥✱ ❍✵ : ♣✶ − ♣✷ = ✵ ❳→❝ ✤à♥❤ ❣✐→ trà ❦✐➸♠ ✤à♥❤ ③= ♣ˆ✶ − ♣ˆ✷ ♣ˆ(✶ − ♣ˆ) ♥✶✶ + ♥✶✷ ♥✶ ♣ˆ✶ + ♥✷ ♣ˆ✷ ♥✶ + ♥✷ ◆➳✉ ♥✶ ✱ ♥✷ ❧ỵ♥✱ ❤❛✐ ♠➝✉ ✤ë❝ ❧➟♣✱ t❛ ❜→❝ ❜ä ❍✵ : = t ự ỵ α t❤❡♦ ✤✐➲✉ ❦✐➺♥ s❛✉ ❤❛② t÷ì♥❣ ✤÷ì♥❣ ♣✲❣✐→ trà ♥❤ä ❤ì♥ α✳ ✈ỵ✐ ♣ ˆ= ●✐↔ t❤✉②➳t ✤è✐ ❍✶ : ♣✶ − ♣✷ > ✵ ❍✶ : ♣✶ − ♣✷ < ✵ ❍✶ : ♣✶ − ♣✷ = ✵ ❇→❝ ❜ä ❍✵ ♥➳✉ ③ > ③α ③ < −③α |③ | > ③α/✷ ♣✲❣✐→ trà P (❩ > ③ ) P (❩ < ③ ) ✷P (❩ > |③ |) ❚r♦♥❣ ❜✐➳♥▲❖◆●✮ ♥❣➝✉ ❇➔✐ ♥❤✐➯♥ ♣❤➙♥ ♣❤è✐❦➯ ❝❤✉➞♥ P❤❛♥ õ ỗ st ố ù♥❣ ❞ö♥❣❤â❛✳◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✵ ✴ ✾✶ ❱➼ ❞ư ▼ët ❝ỉ♥❣ t② ❞÷đ❝ ✤❛♥❣ t❤û ♥❣❤✐➺♠ ❤❛✐ ❧♦↕✐ t❤✉è❝ ❧➔♠ ❣✐↔♠ ❤✉②➳t →♣✳ ❱✐➺❝ t❤û ♥❣❤✐➺♠ t✐➳♥ ❤➔♥❤ tr➯♥ ❤❛✐ ♥❤â♠ ❝♦♥ ✈➟t✳ ◆❤â♠✶✿ ✼✶ ❝♦♥ ❣✐↔♠ ❤✉②➳t →♣ tr♦♥❣ sè ✶✵✵ ❝♦♥ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✶✱ ♥❤â♠ ✷✿ ✺✽ ❝♦♥ ❣✐↔♠ ❤✉②➳t →♣ tr♦♥❣ sè ✾✵ ❝♦♥ ❞ị♥❣ t❤✉è❝ ❧♦↕✐ ✷✳ ❈ỉ♥❣ t② ♠✉è♥ ❦✐➸♠ ✤à♥❤ ự ỵ % õ sỹ t ✈➲ ❤✐➺✉ q✉↔ ❝õ❛ ❤❛✐ ❧♦↕✐ t❤✉è❝ ♥➔② ❦❤ỉ♥❣✳ ▲í✐ ❣✐↔✐✿ ♣✶ ✱ ♣✷ ❧➔ t✛ ❧➺ sè ♣❤➛♥ tû ❣✐↔♠ ❤✉②➳t →♣ ❦❤✐ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✶✱ ✷✳ ❍✵ : ♣✶ − ♣✷ = ✵✱ ❍✶ : ♣✶ − ♣✷ = ✵ ✼✶+✺✽ = ✵.✻✽ ❱➟② ✷ ❚❛ ❝â ♣ˆ✶ = ✵.✼✶✱ ♣ˆ✷ = ✵.✻✹ ♥➯♥ ♣ ˆ = ✶✵✵ +✾✵ ♣ˆ✶ −♣ˆ✷ ✵.✼✶−✵.✻✹ ③= = = ✶.✵✸ ✶ +✶ ) ✵.✻✽(✶−✵.✻✽) ✶✵✵ ♣ˆ(✶−ˆ♣ ♥✶✶ + ♥✶✷ ) ✾✵ ✶ ●å✐ ✸ α = ✺% ♥➯♥ ③α/✷ = ③✵.✵✷✺ = ✶.✾✻ ✹ ❉♦ |③ | = ✶.✵✸ < ✶.✾✻ ổ ọ P ỗ t ự ỵ % st ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✶ ✴ ✾✶ ❱➼ ❞ư ▼ët ❝ỉ♥❣ t② ❞÷đ❝ ✤❛♥❣ t❤û ♥❣❤✐➺♠ ❤❛✐ ❧♦↕✐ t❤✉è❝ ❧➔♠ ❣✐↔♠ ❤✉②➳t →♣✳ ❱✐➺❝ t❤û ♥❣❤✐➺♠ t✐➳♥ ❤➔♥❤ tr➯♥ ❤❛✐ ♥❤â♠ ❝♦♥ ✈➟t✳ ◆❤â♠✶✿ ✼✶ ❝♦♥ ❣✐↔♠ ❤✉②➳t →♣ tr♦♥❣ sè ✶✵✵ ❝♦♥ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✶✱ ♥❤â♠ ✷✿ ✺✽ ❝♦♥ ❣✐↔♠ ❤✉②➳t →♣ tr♦♥❣ sè ✾✵ ❝♦♥ ❞ị♥❣ t❤✉è❝ ❧♦↕✐ ✷✳ ❈ỉ♥❣ t ố ự ỵ % ❝â sü ❦❤→❝ ❜✐➺t ✈➲ ❤✐➺✉ q✉↔ ❝õ❛ ❤❛✐ ❧♦↕✐ t❤✉è❝ ♥➔② ❦❤ỉ♥❣✳ ▲í✐ ❣✐↔✐✿ ♣✶ ✱ ♣✷ ❧➔ t✛ ❧➺ sè ♣❤➛♥ tû ❣✐↔♠ ❤✉②➳t →♣ ❦❤✐ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✶✱ ✷✳ ❍✵ : ♣✶ − ♣✷ = ✵✱ ❍✶ : ♣✶ − ♣✷ = ✵ ✼✶+✺✽ = ✵.✻✽ ❱➟② ✷ ❚❛ ❝â ♣ˆ✶ = ✵.✼✶✱ ♣ˆ✷ = ✵.✻✹ ♥➯♥ ♣ ˆ = ✶✵✵ +✾✵ ♣ˆ✶ −♣ˆ✷ ✵.✼✶−✵.✻✹ ③= = = ✶.✵✸ ✶ +✶ ) ✵.✻✽(✶−✵.✻✽) ✶✵✵ ♣ˆ(✶−ˆ♣ ♥✶✶ + ♥✶✷ ) ✾✵ ✶ ●å✐ ✸ α = ✺% ♥➯♥ ③α/✷ = ③✵.✵✷✺ = ✶.✾✻ ✹ ❉♦ |③ | = ✶.✵✸ < ✶.✾✻ ♥➯♥ ❦❤æ♥❣ ❜→❝ ❜ä P❤❛♥ ❚❤❛♥❤ ỗ t ự ỵ % ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✶ ✴ ✾✶ ❱➼ ❞ö ▼ët ❝ỉ♥❣ t② ❞÷đ❝ ✤❛♥❣ t❤û ♥❣❤✐➺♠ ❤❛✐ ❧♦↕✐ t❤✉è❝ ❧➔♠ ❣✐↔♠ ❤✉②➳t →♣✳ ❱✐➺❝ t❤û ♥❣❤✐➺♠ t✐➳♥ ❤➔♥❤ tr➯♥ ❤❛✐ ♥❤â♠ ❝♦♥ ✈➟t✳ ◆❤â♠✶✿ ✼✶ ❝♦♥ ❣✐↔♠ ❤✉②➳t →♣ tr♦♥❣ sè ✶✵✵ ❝♦♥ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✶✱ ♥❤â♠ ✷✿ ✺✽ ❝♦♥ ❣✐↔♠ ❤✉②➳t →♣ tr♦♥❣ sè ✾✵ ❝♦♥ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✷✳ ❈æ♥❣ t② ♠✉è♥ ❦✐➸♠ ✤à♥❤ ð ♠ù❝ þ ♥❣❤➽❛ ✺% ①❡♠ ❝â sü ❦❤→❝ ❜✐➺t ✈➲ ❤✐➺✉ q✉↔ ❝õ❛ ❤❛✐ ❧♦↕✐ t❤✉è❝ ♥➔② ❦❤ỉ♥❣✳ ▲í✐ ❣✐↔✐✿ ♣✶ ✱ ♣✷ ❧➔ t✛ ❧➺ sè ♣❤➛♥ tû ❣✐↔♠ ❤✉②➳t →♣ ❦❤✐ ❞ò♥❣ t❤✉è❝ ❧♦↕✐ ✶✱ ✷✳ ❍✵ : ♣✶ − ♣✷ = ✵✱ ❍✶ : ♣✶ − ♣✷ = ✵ ✼✶+✺✽ = ✵.✻✽ ❱➟② ✷ ❚❛ ❝â ♣ˆ✶ = ✵.✼✶✱ ♣ˆ✷ = ✵.✻✹ ♥➯♥ ♣ ˆ = ✶✵✵ +✾✵ ♣ˆ✶ −♣ˆ✷ ✵.✼✶−✵.✻✹ ③= = = ✶.✵✸ ✶ +✶ ) ✵.✻✽(✶−✵.✻✽) ✶✵✵ ♣ˆ(✶−ˆ♣ ♥✶✶ + ♥✶✷ ) ✾✵ ✶ ●å✐ ✸ α = ✺% ♥➯♥ ③α/✷ = ③✵.✵✷✺ = ✶.✾✻ ✹ ❉♦ |③ | = ✶.✵✸ < ✶.✾✻ ♥➯♥ ❦❤æ♥❣ ọ P ỗ t ự ỵ % st ố ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✶ ✴ ✾✶ ❑✐➸♠ ✤à♥❤ sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❤❛✐ t✛ ❧➺ tr♦♥❣ ❘ ♣r♦♣✳t❡st✭①✱ ②✱ ❛❧t❡r♥❛t✐✈❡ ❂ ❝✭✧t✇♦✳s✐❞❡❞✧✱✧❧❡ss✧✱✧❣r❡❛t❡r✧✮✱ ❝♦rr❡❝t ❂ r õ trt P ỗ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ✈❡❝t♦ ❝❤ù❛ ❤❛✐ ❣✐→ trà ❧➔ sè ♣❤➛♥ tû ❝â t➼♥❤ ❝❤➜t ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ ♠➝✉ ✶✱ ♠➝✉ ✷ ✈❡❝t♦ ❝❤ù❛ ❤❛✐ ❣✐→ trà ❧➔ ❝ï ❝õ❛ ♠➝✉ ✶✱ ♠➝✉ ✷ ❣✐↔ t❤✉②➳t ✤è✐ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✷ ✴ ✾✶ P❤➙♥ ♣❤è✐ ❋ ❚❛ ❝➛♥ s♦ s→♥❤ ❤❛✐ ♣❤÷ì♥❣ s❛✐ σ✶✷ ✈➔ σ✷✷ ❝õ❛ ❤❛✐ tê♥❣ t❤➸ ❜➡♥❣ ✈✐➺❝ ❦✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ❍✵ : σ✶✷ = σ✷✷ ✈ỵ✐ ❣✐↔ t❤✉②➳t ✤è✐ ❍✶ : σ✶✷ > σ✷✷ ✳ ❚❛ ❜✐➳♥ ✤ê✐ ❝➦♣ ❣✐↔ t❤✉②➳t ♥➔② ♥❤÷ s❛✉ σ✷ σ✷ ❍✵ : ✶✷ = ✶ ✈➔ ❍✶ : ✶✷ > ✶ σ✷ σ✷ ❈❤å♥ tø ❤❛✐ tê♥❣ t❤➸ ❤❛✐ ♠➝✉ ♥❣➝✉ ♥❤✐➯♥ ❝ï ♥✶ ✱ ♥✷ ✳ ❙✶✷ ✈➔ ❙✷✷ ❧➔ ♣❤÷ì♥❣ s❛✐ ♠➝✉✳ ◆➳✉ ❤❛✐ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ t❤➻ ❙✶✷ ❝â ♣❤➙♥ ♣❤è✐ ❋ ✈ỵ✐ ❙✷✷ ♥✶ − ✶ ❜➟❝ tü ❞♦ ð tû ✈➔ ♥✷ − ✶ ❜➟❝ tü ❞♦ ð ♠➝✉✳ P ỗ st ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✸ ✴ ✾✶ P❤➙♥ ♣❤è✐ ❋ Duong phan phoi F voi bac tu n, m P❤❛♥ ❚❤❛♥❤ ỗ Fn,m, s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✹ ✴ ✾✶ ●✐→ trà ❋♥,♠,α ●✐→ trà ❋♥,♠,α ❧➔ ❣✐→ trà s❛♦ ❝❤♦ P (❋♥,♠ > ❋♥,♠,α ) = α tr♦♥❣ ✤â ❋♥,♠ ♣❤➙♥ ♣❤è✐ ❋ ✈ỵ✐ ♥ ❜➟❝ tü ❞♦ ð tû✱ ♠ ❜➟❝ tü ❞♦ P ỗ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✺ ✴ ✾✶ ❑✐➸♠ ✤à♥❤ sü ❜➡♥❣ ♥❤❛✉ ❝õ❛ ❤❛✐ ♣❤÷ì♥❣ s❛✐ ❍✵ : σ✶✷ = σ✷✷ ●✐↔ sû ❤❛✐ ♠➝✉ ♥❣➝✉ ♥❤✐➯♥ ✤ë❝ ❧➟♣ ❝❤å♥ r❛ tø ❤❛✐ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✶ ❱ỵ✐ ❣✐↔ t❤✉②➳t ✤è✐ ❍✶ : σ✶✷ > σ✷✷ ✱ ①→❝ ✤à♥❤ ❣✐→ trà ❦✐➸♠ ✤à♥❤ s✷ ❋ = ✶✷ s✷ ✈➔ ♣✲❣✐→ trà ❧➔ P (❋♥✶ −✶,♥✷ −✶ > ❋ )✳ ❚❛ ❜→❝ ❜ä ❍✵ : σ✶✷ = σ✷✷ t↕✐ ♠ù❝ þ ♥❣❤➽❛ α ♥➳✉ ✶ ❋ > ❋♥✶ −✶,♥✷ −✶,α ❤♦➦❝ t÷ì♥❣ ✤÷ì♥❣ ✷ ♣✲❣✐→ trà ♥❤ä ❤ì♥ α ❚r♦♥❣ ✤â ❋♥✶ −✶,♥✷ −✶ ♣❤➙♥ ♣❤è✐ ❋ ✈ỵ✐ ❜➟❝ tü ❞♦ ð tû ♥✶ − ✶ ✈➔ ❜➟❝ tü ❞♦ P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✻ ✴ ✾✶ ❑✐➸♠ ✤à♥❤ sü ❜➡♥❣ ♥❤❛✉ ❝õ❛ ❤❛✐ ♣❤÷ì♥❣ s❛✐ ❍✵ : σ✶✷ = σ✷✷ ✷ ❱ỵ✐ ❣✐↔ t❤✉②➳t ✤è✐ ❍✶ : σ✶✷ < σ✷✷ ✱ ①→❝ ✤à♥❤ ❣✐→ trà ❦✐➸♠ ✤à♥❤ s✷ ❋ = ✷✷ s✶ ✈➔ ♣✲❣✐→ trà ❧➔ P (❋♥✷ −✶,♥✶ −✶ > ❋ )✳ ❚❛ ❜→❝ ❜ä ❍✵ : = t ự ỵ ✶ ❋ > ❋♥✷ −✶,♥✶ −✶,α ❤♦➦❝ t÷ì♥❣ ✤÷ì♥❣ ✷ ♣✲❣✐→ trà ♥❤ä ❤ì♥ α ❚r♦♥❣ ✤â ❋♥✷ −✶,♥✶ −✶ ♣❤➙♥ ♣❤è✐ ❋ ✈ỵ✐ ❜➟❝ tü ❞♦ ð tû ♥✷ − ✶ ✈➔ ❜➟❝ tü ❞♦ ð ♠➝✉ ♥✶ − P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✼ ✴ ✾✶ ❑✐➸♠ ✤à♥❤ sü ❜➡♥❣ ♥❤❛✉ ❝õ❛ ❤❛✐ ♣❤÷ì♥❣ s❛✐ ❍✵ : σ✶✷ = σ✷✷ ✸ ❱ỵ✐ ❣✐↔ t❤✉②➳t ✤è✐ ❍✶ : σ✶✷ = σ✷✷ ✱ ♥➳✉ s✶✷ > s✷✷ ✱ ①→❝ ✤à♥❤ ❣✐→ trà ❦✐➸♠ ✤à♥❤ s✷ ❋ = ✶✷ s✷ ✈➔ ♣✲❣✐→ trà ❧➔ ✷P (❋♥✶ −✶,♥✷ −✶ > ❋ )✳ ❚❛ ❜→❝ ❜ä : = t ự ỵ ♥➳✉ ✶ ❋ > ❋♥✶ −✶,♥✷ −✶,α/✷ ❤❛② ❋ > ❋♥✶ −✶,♥✷ −✶,✶−α/✷ ✱ ❤♦➦❝ t÷ì♥❣ ✤÷ì♥❣ ✷ ♣✲❣✐→ trà ♥❤ä ❤ì♥ α ❚r♦♥❣ ✤â ❋♥✷ −✶,♥✶ −✶ ♣❤➙♥ ♣❤è✐ ❋ ✈ỵ✐ ❜➟❝ tü ❞♦ ð tû ♥✷ − ✶ ✈➔ ❜➟❝ tü ❞♦ ð ♠➝✉ ♥✶ − ✶✳ P❤❛♥ ỗ st ố ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✽ ✴ ✾✶ ❱➼ ❞ư ▼ët ❝ỉ♥❣ t② ❞ị♥❣ ❤❛✐ ❧♦↕✐ ❝❤➜t ①ó❝ t→❝ ❆✱ ❇ t❤❛♠ ❣✐❛ q✉→ tr➻♥❤ ①↔♥ s✉➜t ♠ët s↔♥ ♣❤➞♠ ❤â❛ ❤å❝✳ ❍å ♠✉è♥ s♦ s→♥❤ ♣❤÷ì♥❣ s❛✐ ❝õ❛ sè s↔♥ ♣❤➞♠ s↔♥ ①✉➜t ✤÷đ❝ tr♦♥❣ ♠ët ❣✐í ❦❤✐ ❞ị♥❣ ♠é✐ ❧♦↕✐ ❝❤➜t ①ó❝ t→❝ ✤â✳ ❈❤å♥ ♥❣➝✉ ♥❤✐➯♥ ✺ ❧➛♥ s↔♥ s✉➜t ❦➨♦ ❞➔✐ ✶❤ t÷ì♥❣ ù♥❣ sû ❞ư♥❣ ♠é✐ ❝❤➝t ①ó❝ t→❝ tr➯♥✳ ❙è s↔♥ ♣❤➞♠ t❤✉ ✤÷đ❝ ♥❤÷ s❛✉ ❈❤➜t ❆ ✽✵✶ ✽✶✹ ✼✽✹ ✽✸✻ ✽✷✵ ❈❤➜t ❇ ✼✺✷ ✼✶✽ ✼✼✻ ✼✹✷ ✼✻✸ ●✐↔ sû sè s↔♥ ♣❤➞♠ s↔♥ ①✉➜t ✤÷đ❝ tr♦♥❣ ♠ët ❣✐í ❞ị♥❣ ❝❤➜t ❆✱ ❝❤➜t ❇ ❝â ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✳ ◆❣÷í✐ t❛ ❝❤♦ r➡♥❣ ♣❤÷ì♥❣ s❛✐ ❝õ❛ sè s↔♥ ♣❤➞♠ ù♥❣ ✈ỵ✐ ❝❤➜t ❆ ✭σ✶✷ ✮♥❤ä ❤ì♥ ❝❤➜t ❇ ✭σ✷✷ ✮✳ ❍➣② ❦✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ♥➔② t↕✐ ♠ù❝ ỵ P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✽✾ ✴ ✾✶ ❱➼ ❞ö ✶ ●✐↔ t❤✉②➳t ✈➔ ❣✐↔ t❤✉②➳t ✤è✐✿ ❍✵ : σ✶✷ = σ✷✷ ❍✶ : σ✶✷ < σ✷✷ s✷ s✶✷ = ✸✽✻✱ s✷✷ = ✹✽✹.✷ ✈➟② ❋ = s✷✷ = ✹✽✹.✷/✸✽✻ = ✶.✷✺✹✹ ✶ ✸ ❱ỵ✐ α = ✺%✱ t❛ ❝â ❋♥✶ −✶,♥✷ −✶,α = ❋✹,✹,✵.✵✺ = ✻.✸✽✽ ✹ ❉♦ ❋ < ❋✹,✹,✵.✵✺ ✳ ❱➟② t❛ ❦❤æ♥❣ ❜→❝ ❜ä ❍✵ ð ♠ù❝ ỵ . ữủ P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✾✵ ✴ ✾✶ ❑✐➸♠ ✤à♥❤ sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❤❛✐ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘ ✈❛r✳t❡st✭①✱ ②✱ ❛❧t❡r♥❛t✐✈❡❂❝✭✧t✇♦✳s✐❞❡❞✧✱✧❧❡ss✧✱✧❣r❡❛t❡r✧✮✮ ❚r♦♥❣ ✤â ①✱ ②✿ ❛❧t❡r♥❛t✐✈❡✿ P❤❛♥ ỗ t ỳ ✶✱ ♠➝✉ ✷ ❣✐↔ t❤✉②➳t ✤è✐ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✷✽ t❤→♥❣ ✹ ♥➠♠ ✷✵✵✾ ✾✶ ✴ ✾✶

Ngày đăng: 10/02/2022, 18:18

Mục lục

    Kim inh gia thuyt v tham s cua mt tng th

    Mt s khái nim

    Kim inh gia thuyt v trung bình tng th

    Kim inh gia thuyt v trung bình tng th phân phi chun, bit phng sai tng th

    Kim inh gia thuyt v trung bình tng th, c mu nho

    Kim inh gia thuyt v ty l tng th

    Kim inh gia thuyt v phng sai tng th

    Kim inh gia thuyt v hai tng th

    Kim inh gia thuyt cho s khác bit cua hai trung bình tng th

    KÐGT cho s khác bit cua hai trung bình tng th, bit phng sai hai tng th (hoc c mu ln), hai mu c lp

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