Bài giảng xác suất thống kê ứng dụng trong kinh tế xã hội chương 10 phân tích phương sai

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Bài giảng xác suất thống kê ứng dụng trong kinh tế xã hội   chương 10  phân tích phương sai

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❈❤÷ì♥❣ ❳ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❇ë ♠ỉ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✻ ✴ ✻✻✹ ❈❤÷ì♥❣ ❳ ✸✹ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ❙♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ❙♦ s→♥❤ ♣❤÷ì♥❣ s❛✐ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ✸✺ P❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ✸✻ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ❚r÷í♥❣ ❤đ♣ ❝â ♠ët q✉❛♥ s→t tr♦♥❣ ♠ët ỉ ❚r÷í♥❣ ❤đ♣ ♥❤✐➲✉ q✉❛♥ s→t tr♦♥❣ ♠ët æ ✸✼ P❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✼ ✴ ✻✻✹ ❈❤÷ì♥❣ ❳ ✸✹ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ❙♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ❙♦ s→♥❤ ♣❤÷ì♥❣ s❛✐ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ✸✺ P❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ✸✻ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ❚r÷í♥❣ ❤đ♣ ❝â ♠ët q✉❛♥ s→t tr♦♥❣ ♠ët ỉ ❚r÷í♥❣ ❤đ♣ ♥❤✐➲✉ q✉❛♥ s→t tr♦♥❣ ♠ët ỉ ✸✼ P❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✼ ✴ ✻✻✹ ❈❤÷ì♥❣ ❳ ✸✹ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ❙♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ❙♦ s→♥❤ ♣❤÷ì♥❣ s❛✐ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ✸✺ P❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ✸✻ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ❚r÷í♥❣ ❤đ♣ ❝â ♠ët q✉❛♥ s→t tr♦♥❣ ♠ët ỉ ❚r÷í♥❣ ❤đ♣ ♥❤✐➲✉ q✉❛♥ s→t tr♦♥❣ ♠ët æ ✸✼ P❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✼ ✴ ✻✻✹ ❈❤÷ì♥❣ ❳ ✸✹ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ❙♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ❙♦ s→♥❤ ♣❤÷ì♥❣ s❛✐ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ✸✺ P❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ✸✻ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ❚r÷í♥❣ ❤đ♣ ❝â ♠ët q✉❛♥ s→t tr♦♥❣ ♠ët ỉ ❚r÷í♥❣ ❤đ♣ ♥❤✐➲✉ q✉❛♥ s→t tr♦♥❣ ♠ët æ ✸✼ P❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✼ ✴ ✻✻✹ ◆ë✐ ❞✉♥❣ tr➻♥❤ ❜➔② ✸✹ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ❙♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ❙♦ s→♥❤ ♣❤÷ì♥❣ s❛✐ ❝õ❛ ♥❤✐➲✉ tê♥❣ t❤➸ ✸✺ P❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ✸✻ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ❚r÷í♥❣ ❤đ♣ ❝â ♠ët q✉❛♥ s→t tr♦♥❣ ♠ët ỉ ❚r÷í♥❣ ❤đ♣ ♥❤✐➲✉ q✉❛♥ s→t tr♦♥❣ ♠ët æ ✸✼ P❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✽ ✴ ✻✻✹ ❇➔✐ t♦→♥ s♦ s→♥❤ ♥❤✐➲✉ tr✉♥❣ ❜➻♥❤ ❇➔✐ t♦→♥ ●✐↔ sû ❝â ❦ tê♥❣ t❤➸ t✉➙♥ t❤❡♦ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥✱ ♣❤÷ì♥❣ s ợ tr ữủt , µ✷ , , µ❦ ✳ ❚❛ ❝➛♥ s♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ❦ tê♥❣ t❤➸ ♥➔② ❞ü❛ tr➯♥ ♥❤ú♥❣ ♠➝✉ ♥❣➝✉ ♥❤✐➯♥ ✤ë❝ ❧➟♣ ❝❤å♥ r❛ tø ❦ tê♥❣ t❤➸ ♥➔② ❜➡♥❣ ❝→❝❤ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ♥❤➙♥ tè ✭❖♥❡✲✇❛② ❆◆❖❱❆✮✱ tù❝ ❧➔ t❛ ❝➛♥ ❦✐➸♠ ✤à♥❤ ❝➦♣ ❣✐↔ t❤✉②➳t ✏ µ✷ ✏ ✏ µ❦ ❍✶ : ❉✐ ✘ ❥ : µ✐ ✘ µ❥ , ✐ , ❥ ✏ ✶, ❦ ✵ : µ✶ ❍ ❇ë ♠ỉ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✹✾ ✴ ✻✻✹ ❇➔✐ t♦→♥ s♦ s→♥❤ ♥❤✐➲✉ tr✉♥❣ ❜➻♥❤ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ♥❤➙♥ tè ✭❖♥❡✲✇❛② ❆◆❖❱❆✮ ❧➔ ♣❤➙♥ t➼❝❤ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ♠ët ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ✭❞↕♥❣ ❜✐➳♥ ✤à♥❤ t➼♥❤✮ ↔♥❤ ❤÷ð♥❣ ✤➳♥ ♠ët ②➳✉ tè ❦➳t q✉↔ ✭❞↕♥❣ ❜✐➳♥ ✤à♥❤ ❧÷đ♥❣✮ ✤❛♥❣ ♥❣❤✐➯♥ ❝ù✉✳ ◆❤ú♥❣ ❣✐↔ ✤à♥❤ ❦❤✐ t✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ ❆◆❖❱❆✿ ❈→❝ tê♥❣ t❤➸ t✉➙♥ t❤❡♦ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥❀ ❈→❝ ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❜➡♥❣ ♥❤❛✉❀ ❈→❝ ♠➝✉ ❝❤å♥ r❛ ✤ë❝ ❧➟♣ ✈ỵ✐ ♥❤❛✉✳ ❇ë ♠ỉ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✺✵ ✴ ✻✻✹ ❇➔✐ t♦→♥ s♦ s→♥❤ ♥❤✐➲✉ tr✉♥❣ ❜➻♥❤ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ♥❤➙♥ tè ✭❖♥❡✲✇❛② ❆◆❖❱❆✮ ❧➔ ♣❤➙♥ t➼❝❤ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ♠ët ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ✭❞↕♥❣ ❜✐➳♥ ✤à♥❤ t➼♥❤✮ ↔♥❤ ❤÷ð♥❣ ✤➳♥ ♠ët ②➳✉ tè ❦➳t q✉↔ ✭❞↕♥❣ ❜✐➳♥ ✤à♥❤ ❧÷đ♥❣✮ ✤❛♥❣ ♥❣❤✐➯♥ ❝ù✉✳ ◆❤ú♥❣ ❣✐↔ ✤à♥❤ ❦❤✐ t✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ ❆◆❖❱❆✿ ❈→❝ tê♥❣ t❤➸ t✉➙♥ t❤❡♦ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥❀ ❈→❝ ♣❤÷ì♥❣ s❛✐ tê♥❣ t❤➸ ❜➡♥❣ ♥❤❛✉❀ ❈→❝ ♠➝✉ ❝❤å♥ r❛ ✤ë❝ ❧➟♣ ✈ỵ✐ ♥❤❛✉✳ ❇ë ♠ỉ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✺✵ ✴ ✻✻✹ ◗✉✐ tr➻♥❤ t❤ü❝ ❤✐➺♥ ❜➔✐ t♦→♥ ♣❤➙♥ t ữỡ s ởt tố ữợ tr✉♥❣ ❜➻♥❤ ♠➝✉✳ ●✐↔ sû t❛ ❝â ❦ ♠➝✉ ✈ỵ✐ sè ♣❤➛♥ tû ❧➛♥ ❧÷đt ❧➔ ♥ , ♥ , , ♥❦ ❝❤å♥ tø ❦ tê♥❣ t❤➸ ữủ ữợ ✶ ①✶✶ ①✷✶ ①✶✷ ①✷✷ ① ♥✶ ① ♥✷ ✶ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ✷ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ✷ ①❦ ✶ ①❦ ✷ ①❦♥❦ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✺✶ ✴ ✻✻✹ ❚❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘ ❚↕♦ t❤ù tü ❝õ❛ ✻✸ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ♠➝✉ ❣ë♣✿ ✐❞ ❂ ✶✿✻✸✳ ◆❤➟♣ ❜è♥ ✈➨❝ tì ❞ú ❧✐➺✉ ♠➝✉✱ ✈➨❝ tì ♣❤➙♥ ❧♦↕✐ t❤❡♦ ♥❤â♠✱ t❤❡♦ ❦❤è✐ ✈➔ ✈➨❝tì ❝❤➾ t❤ù tü ❝→❝ ♣❤➛♥ tû ♠➝✉ ✈➔♦ ♠ët ❞❛t❛✳❢r❛♠❡✿ ❉✉▲✐❡✉ ❂ ❞❛t❛✳❢r❛♠❡✭✐❞✱ ▼❛✉●♦♣✱ P❤❛♥◆❤♦♠✱ P❤❛♥❑❤♦✐✮ ❚✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❜➡♥❣ ❤➔♠ ❛♥♦✈❛✭✮✿ ❛♥♦✈❛✭❧♠✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐✮✮ ✣➸ ①❡♠ ①➨t sü t÷ì♥❣ t→❝ ❝õ❛ ❤❛✐ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ❧➯♥ ②➳✉ tè ❦➳t q✉↔ t❛ t❤ü❝ ❤✐➺♥ ♥❤÷ s❛✉✿ ❛♥♦✈❛✭❧♠✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐ ✰ P❤❛♥◆❤♦♠✯P❤❛♥❑❤♦✐✮✮ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✸ ✴ ✻✻✹ ❚❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘ ❚↕♦ t❤ù tü ❝õ❛ ✻✸ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ♠➝✉ ❣ë♣✿ ✐❞ ❂ ✶✿✻✸✳ ◆❤➟♣ ❜è♥ ✈➨❝ tì ❞ú ❧✐➺✉ ♠➝✉✱ ✈➨❝ tì ♣❤➙♥ ❧♦↕✐ t❤❡♦ ♥❤â♠✱ t❤❡♦ ❦❤è✐ ✈➔ ✈➨❝tì ❝❤➾ t❤ù tü ❝→❝ ♣❤➛♥ tû ♠➝✉ ✈➔♦ ♠ët ❞❛t❛✳❢r❛♠❡✿ ❉✉▲✐❡✉ ❂ ❞❛t❛✳❢r❛♠❡✭✐❞✱ ▼❛✉●♦♣✱ P❤❛♥◆❤♦♠✱ P❤❛♥❑❤♦✐✮ ❚✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❜➡♥❣ ❤➔♠ ❛♥♦✈❛✭✮✿ ❛♥♦✈❛✭❧♠✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐✮✮ ✣➸ ①❡♠ ①➨t sü t÷ì♥❣ t→❝ ❝õ❛ ❤❛✐ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ❧➯♥ ②➳✉ tè ❦➳t q✉↔ t❛ t❤ü❝ ❤✐➺♥ ♥❤÷ s❛✉✿ ❛♥♦✈❛✭❧♠✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐ ✰ P❤❛♥◆❤♦♠✯P❤❛♥❑❤♦✐✮✮ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✸ ✴ ✻✻✹ ❚❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘ ❚↕♦ t❤ù tü ❝õ❛ ✻✸ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ♠➝✉ ❣ë♣✿ ✐❞ ❂ ✶✿✻✸✳ ◆❤➟♣ ❜è♥ ✈➨❝ tì ❞ú ❧✐➺✉ ♠➝✉✱ ✈➨❝ tì ♣❤➙♥ ❧♦↕✐ t❤❡♦ ♥❤â♠✱ t❤❡♦ ❦❤è✐ ✈➔ ✈➨❝tì ❝❤➾ t❤ù tü ❝→❝ ♣❤➛♥ tû ♠➝✉ ✈➔♦ ♠ët ❞❛t❛✳❢r❛♠❡✿ ❉✉▲✐❡✉ ❂ ❞❛t❛✳❢r❛♠❡✭✐❞✱ ▼❛✉●♦♣✱ P❤❛♥◆❤♦♠✱ P❤❛♥❑❤♦✐✮ ❚✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❜➡♥❣ ❤➔♠ ❛♥♦✈❛✭✮✿ ❛♥♦✈❛✭❧♠✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐✮✮ ✣➸ ①❡♠ ①➨t sü t÷ì♥❣ t→❝ ❝õ❛ ❤❛✐ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ❧➯♥ ②➳✉ tè ❦➳t q✉↔ t❛ t❤ü❝ ❤✐➺♥ ♥❤÷ s❛✉✿ ❛♥♦✈❛✭❧♠✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐ ✰ P❤❛♥◆❤♦♠✯P❤❛♥❑❤♦✐✮✮ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✸ ✴ ✻✻✹ ❇➔✐ t♦→♥ ♣❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ❚r♦♥❣ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè✱ ❦❤✐ ✤➣ ①→❝ ✤à♥❤ ✤÷đ❝ ❝â sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❝→❝ ♥❤â♠ s♦ s→♥❤✱ ❝❤ó♥❣ t❛ ❝â t❤➸ ❞ị♥❣ ❦✐➸♠ ✤à♥❤ ❚✉❦❡② ❍❙❉ ✤➸ ①→❝ ✤à♥❤ ❝→❝ ❝➦♣ tr✉♥❣ ❜➻♥❤ ❦❤→❝ ♥❤❛✉ ①➨t t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t ✭s♦ s→♥❤ ❣✐ú❛ ❑ ♥❤â♠✮ ❤❛② ①➨t t❤❡♦ ②➳✉ tè t❤ù ❤❛✐ ✭s♦ s→♥❤ ❣✐ú❛ ố tr ợ ữủ t t❤❡♦ ❝æ♥❣ t❤ù❝✿ ❚ ❚ ✏ qα,❑ ,❑❍ ♣▲✁✶q ✏ qα,❍ ,❑❍ ♣▲✁✶q ❝ ❝ ▼❙❊ ❍ ✂ ▲ ✱ ✤è✐ ✈ỵ✐ ✈✐➺❝ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t❀ ▼❙❊ ❑ ✂ ▲ ✱ ✤è✐ ✈ỵ✐ ✈✐➺❝ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐✳ ✵ ❚✐➯✉ ❝❤✉➞♥ q✉②➳t ✤à♥❤ ❧➔ ❜→❝ ❜ä ❣✐↔ t❤✉②➳t ❍ ❦❤✐ ✤ë ❧➺❝❤ t✉②➺t ✤è✐ ❣✐ú❛ ❝→❝ ❝➦♣ tr✉♥❣ ❜➻♥❤ ♠➝✉ t❤❡♦ ♥❤â♠ ✭❞á♥❣✮ ợ ỡ ợ tữỡ ự ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✹ ✴ ✻✻✹ ❇➔✐ t♦→♥ ♣❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ❚r♦♥❣ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè✱ ❦❤✐ ✤➣ ①→❝ ✤à♥❤ ✤÷đ❝ ❝â sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❝→❝ ♥❤â♠ s♦ s→♥❤✱ ❝❤ó♥❣ t❛ ❝â t❤➸ ❞ò♥❣ ❦✐➸♠ ✤à♥❤ ❚✉❦❡② ❍❙❉ ✤➸ ①→❝ ✤à♥❤ ❝→❝ ❝➦♣ tr✉♥❣ ❜➻♥❤ ❦❤→❝ ♥❤❛✉ ①➨t t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t ✭s♦ s→♥❤ ❣✐ú❛ ❑ ♥❤â♠✮ ❤❛② ①➨t t❤❡♦ ②➳✉ tè t❤ù ❤❛✐ ✭s♦ s→♥❤ ❣✐ú❛ ❍ ❦❤è✐✮✳ tr ợ ữủ t t ổ t❤ù❝✿ ❚ ❚ ✏ qα,❑ ,❑❍ ♣▲✁✶q ✏ qα,❍ ,❑❍ ♣▲✁✶q ❝ ❝ ▼❙❊ ❍ ✂ ▲ ✱ ✤è✐ ✈ỵ✐ ✈✐➺❝ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t❀ ▼❙❊ ❑ ✂ ▲ ✱ ✤è✐ ✈ỵ✐ ✈✐➺❝ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐✳ ✵ ❚✐➯✉ ❝❤✉➞♥ q✉②➳t ✤à♥❤ ❧➔ ❜→❝ ❜ä ❣✐↔ t❤✉②➳t ❍ ❦❤✐ ✤ë ❧➺❝❤ t✉②➺t ✤è✐ ❣✐ú❛ ❝→❝ ❝➦♣ tr✉♥❣ ❜➻♥❤ ♠➝✉ t❤❡♦ ♥❤â♠ ✭❞á♥❣✮ ❧ỵ♥ ❤ì♥ ợ tữỡ ự ổ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✹ ✴ ✻✻✹ ❇➔✐ t♦→♥ ♣❤➙♥ t➼❝❤ s➙✉ ❖♥❡✲✇❛② ❆◆❖❱❆ ❚r♦♥❣ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè✱ ❦❤✐ ✤➣ ①→❝ ✤à♥❤ ✤÷đ❝ ❝â sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❝→❝ ♥❤â♠ s♦ s→♥❤✱ ❝❤ó♥❣ t❛ ❝â t❤➸ ❞ò♥❣ ❦✐➸♠ ✤à♥❤ ❚✉❦❡② ❍❙❉ ✤➸ ①→❝ ✤à♥❤ ❝→❝ ❝➦♣ tr✉♥❣ ❜➻♥❤ ❦❤→❝ ♥❤❛✉ ①➨t t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t ✭s♦ s→♥❤ ❣✐ú❛ ❑ ♥❤â♠✮ ❤❛② ①➨t t❤❡♦ ②➳✉ tè t❤ù ❤❛✐ ✭s♦ s→♥❤ ❣✐ú❛ ❍ ❦❤è✐✮✳ ❍❛✐ ❣✐→ tr ợ ữủ t t ổ tự ❚ ✏ qα,❑ ,❑❍ ♣▲✁✶q ✏ qα,❍ ,❑❍ ♣▲✁✶q ❝ ❝ ▼❙❊ ❍ ✂ ▲ ✱ ✤è✐ ✈ỵ✐ ✈✐➺❝ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t❀ ▼❙❊ ❑ ✂ ▲ ✱ ✤è✐ ✈ỵ✐ ✈✐➺❝ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐✳ ✵ ❚✐➯✉ ❝❤✉➞♥ q✉②➳t ✤à♥❤ ❧➔ ❜→❝ ❜ä ❣✐↔ t❤✉②➳t ❍ ❦❤✐ ✤ë ❧➺❝❤ t✉②➺t ✤è✐ ❣✐ú❛ ❝→❝ ❝➦♣ tr✉♥❣ ❜➻♥❤ ♠➝✉ t❤❡♦ ♥❤â♠ ✭❞á♥❣✮ ❧ỵ♥ ❤ì♥ ❤❛② ❜➡♥❣ ợ tữỡ ự ổ ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✹ ✴ ✻✻✹ ❱➼ ❞ö ✏ ✸, ❍ ✏ ✸, ▲ ✏ ✼, α ✏ ✺%, ▼❙❊ ✏ ✵.✶✷✽✳ ✵ ✵✺,✸,✺✹ ✏ ✸.✹✳ ❚r♦♥❣ t➼♥❤ t♦→♥ ð ✈➼ ❞ö tr➯♥✱ t❛ ❝â ❑ ●✐→ trà q ❝õ❛ ♣❤➙♥ ♣❤è✐ ❚✉❦❡②✿ q ❙♦ s→♥❤ ❣✐ú❛ ❝→❝ ♥❤â♠ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t ✭t❤í✐ ❣✐❛♥ tü ❤å❝✮✱ ❣✐→ trà tỵ✐ ❤↕♥✿ ❚ ✏ ✸.✵✹ ❝ ✵.✶✷✽ ✷✶ ✏ ✵.✷✻✺✳ ❚r✉♥❣ ❜➻♥❤ ♥❤â♠ ❧➛♥ ❧÷đt ❧➔✿ ✺.✼, ✻.✹, ✻.✽ ✈➔ ❝❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ❝→❝ ♥❤â♠ ❧➔ ✏ ⑤✺.✼ ✁ ✻.✹⑤ ✏ ✵.✼❀ ✏ ⑤✺.✼ ✁ ✻.✽⑤ ✏ ✶.✶❀ ✏ ⑤✻.✹ ✁ ✻.✽⑤ ✏ ✵.✹✳ ❉➼t✱ ❚❇ ❉➼t✱ ♥❤✐➲✉ ❉❚❇✱ ♥❤✐➲✉ ❈→❝ ❝❤➯♥❤ ❧➺❝❤ ✤➲✉ ❧ỵ♥ ❤ì♥ ❣✐→ trà ❣✐ỵ✐ ❤↕♥ ❚✉❦❡② ❚✱ ❝❤♦ ♥➯♥ t❛ ❝â t❤➸ ❦➳t ❧✉➟♥ r➡♥❣ s✐♥❤ ✈✐➯♥ ❝â t❤í✐ ❣✐❛♥ tü ❤å❝ ❦❤→❝ ♥❤❛✉ ❝â ✤✐➸♠ tr✉♥❣ ❜➻♥❤ ❤å❝ t➟♣ ❦❤→❝ ♥❤❛✉✳ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✺ ✴ ✻✻✹ ❱➼ ❞ö ✏ ✸, ❍ ✏ ✸, ▲ ✏ ✼, α ✏ ✺%, ▼❙❊ ✏ ✵.✶✷✽✳ ✵ ✵✺,✸,✺✹ ✏ ✸.✹✳ ❚r♦♥❣ t➼♥❤ t♦→♥ ð ✈➼ ❞ö tr➯♥✱ t❛ ❝â ❑ ●✐→ trà q ❝õ❛ ♣❤➙♥ ♣❤è✐ ❚✉❦❡②✿ q ❙♦ s→♥❤ ❣✐ú❛ ❝→❝ ♥❤â♠ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t ✭t❤í✐ ❣✐❛♥ tü ❤å❝✮✱ ❣✐→ trà tỵ✐ ❤↕♥✿ ❚ ✏ ✸.✵✹ ❝ ✵.✶✷✽ ✷✶ ✏ ✵.✷✻✺✳ ❚r✉♥❣ ❜➻♥❤ ♥❤â♠ ❧➛♥ ❧÷đt ❧➔✿ ✺.✼, ✻.✹, ✻.✽ ✈➔ ❝❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ❝→❝ ♥❤â♠ ❧➔ ✏ ⑤✺.✼ ✁ ✻.✹⑤ ✏ ✵.✼❀ ✏ ⑤✺.✼ ✁ ✻.✽⑤ ✏ ✶.✶❀ ✏ ⑤✻.✹ ✁ ✻.✽⑤ ✏ ✵.✹✳ ❉➼t✱ ❚❇ ❉➼t✱ ♥❤✐➲✉ ❉❚❇✱ ♥❤✐➲✉ ❈→❝ ❝❤➯♥❤ ❧➺❝❤ ✤➲✉ ❧ỵ♥ ❤ì♥ ❣✐→ trà ❣✐ỵ✐ ❤↕♥ ❚✉❦❡② ❚✱ ❝❤♦ ♥➯♥ t❛ ❝â t❤➸ ❦➳t ❧✉➟♥ r➡♥❣ s✐♥❤ ✈✐➯♥ ❝â t❤í✐ ❣✐❛♥ tü ❤å❝ ❦❤→❝ ♥❤❛✉ ❝â ✤✐➸♠ tr✉♥❣ ❜➻♥❤ ❤å❝ t➟♣ ❦❤→❝ ♥❤❛✉✳ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✺ ✴ ✻✻✹ ❱➼ ❞ö ✏ ✸, ❍ ✏ ✸, ▲ ✏ ✼, α ✏ ✺%, ▼❙❊ ✏ ✵.✶✷✽✳ ✵ ✵✺,✸,✺✹ ✏ ✸.✹✳ ❚r♦♥❣ t➼♥❤ t♦→♥ ð ✈➼ ❞ö tr➯♥✱ t❛ ❝â ❑ ●✐→ trà q ❝õ❛ ♣❤➙♥ ♣❤è✐ ❚✉❦❡②✿ q ❙♦ s→♥❤ ❣✐ú❛ ❝→❝ ♥❤â♠ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t ✭t❤í✐ ❣✐❛♥ tü ❤å❝✮✱ ❣✐→ trà tỵ✐ ❤↕♥✿ ❚ ✏ ✸.✵✹ ❝ ✵.✶✷✽ ✷✶ ✏ ✵.✷✻✺✳ ❚r✉♥❣ ❜➻♥❤ ♥❤â♠ ❧➛♥ ❧÷đt ❧➔✿ ✺.✼, ✻.✹, ✻.✽ ✈➔ ❝❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ❝→❝ ♥❤â♠ ❧➔ ✏ ⑤✺.✼ ✁ ✻.✹⑤ ✏ ✵.✼❀ ✏ ⑤✺.✼ ✁ ✻.✽⑤ ✏ ✶.✶❀ ✏ ⑤✻.✹ ✁ ✻.✽⑤ ✏ ✵.✹✳ ❉➼t✱ ❚❇ ❉➼t✱ ♥❤✐➲✉ ❉❚❇✱ ♥❤✐➲✉ ❈→❝ ❝❤➯♥❤ ❧➺❝❤ ✤➲✉ ❧ỵ♥ ❤ì♥ ❣✐→ trà ❣✐ỵ✐ ❤↕♥ ❚✉❦❡② ❚✱ ❝❤♦ ♥➯♥ t❛ ❝â t❤➸ ❦➳t ❧✉➟♥ r➡♥❣ s✐♥❤ ✈✐➯♥ ❝â t❤í✐ ❣✐❛♥ tü ❤å❝ ❦❤→❝ ♥❤❛✉ ❝â ✤✐➸♠ tr✉♥❣ ❜➻♥❤ ❤å❝ t➟♣ ❦❤→❝ ♥❤❛✉✳ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✺ ✴ ✻✻✹ ❱➼ ❞ö ❙♦ s→♥❤ ❣✐ú❛ ❝→❝ ♥❤â♠ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐ ✭♠ù❝ ✤ë ②➯✉ t❤➼❝❤ ♥❣➔♥❤ ❤å❝✮✱ ❣✐→ trà tỵ✐ ❤↕♥✿ ❚ ✏ ✸.✵✹ ❝ ✵.✶✷✽ ✷✶ ✏ ✵.✷✻✺✳ ❚r✉♥❣ ❜➻♥❤ ❦❤è✐ ❧➛♥ ❧÷đt ❧➔✿ ✺.✾✸, ✻.✸✻, ✻.✻ ✈➔ ❝❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ❝→❝ ❦❤è✐ ❧➔ ✏ ⑤✺.✾✸ ✁ ✻.✸✻⑤ ✏ ✵.✹✸❀ ✏ ⑤✺.✾✸ ✁ ✻.✻⑤ ✏ ✵.✻✼❀ ✏ ⑤✻.✸✻ ✁ ✻.✻⑤ ✏ ✵.✷✹✳ ❉❦❤æ♥❣ t❤➼❝❤✱ t❤➼❝❤ ❉❦❤æ♥❣ t❤➼❝❤✱ r➜t t❤➼❝❤ ❉t❤➼❝❤✱ r➜t t❤➼❝❤ t❤➼❝❤✱ r➜t t❤➼❝❤ ❈❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ♥❤â♠ t❤➼❝❤ ✈➔ r➜t t❤➼❝❤ ❉ ♥❤ä ❤ì♥ ❣✐→ trà ❚ ❣✐ỵ✐ ❤↕♥✱ ♥➯♥ t❛ ❦➳t ❧✉➟♥ r➡♥❣ ♥❤â♠ s✐♥❤ ✈✐➯♥ ❝â ♠ù❝ ✤ë ②➯✉ t❤➼❝❤ ♥❣➔♥❤ ❤å❝ ♥❤✐➲✉ ❤❛② r➜t ♥❤✐➲✉ t❤➻ ❦➳t q✉↔ ❤å❝ t➟♣ ❦❤æ♥❣ ❦❤→❝ ❜✐➺t ♥❤❛✉ ✤→♥❣ ❦➸✳ ◆❤â♠ ❦❤æ♥❣ t❤➼❝❤ ♥❣➔♥❤ ❤å❝ ❝â ❦➳t q✉↔ ❤å❝ t➟♣ ❦➨♠ ❤ì♥ ❤➥♥ ❤❛✐ ♥❤â♠ t❤➼❝❤ ✈➔ r➜t t❤➼❝❤ ♥❣➔♥❤ ✤❛♥❣ ❤å❝✳ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✻ ✴ ✻✻✹ ❱➼ ❞ö ❙♦ s→♥❤ ❣✐ú❛ ❝→❝ ♥❤â♠ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐ ✭♠ù❝ ✤ë ②➯✉ t❤➼❝❤ ♥❣➔♥❤ ❤å❝✮✱ ❣✐→ trà tỵ✐ ❤↕♥✿ ❚ ✏ ✸.✵✹ ❝ ✵.✶✷✽ ✷✶ ✏ ✵.✷✻✺✳ ❚r✉♥❣ ❜➻♥❤ ❦❤è✐ ❧➛♥ ❧÷đt ❧➔✿ ✺.✾✸, ✻.✸✻, ✻.✻ ✈➔ ❝❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ❝→❝ ❦❤è✐ ❧➔ ✏ ⑤✺.✾✸ ✁ ✻.✸✻⑤ ✏ ✵.✹✸❀ ✏ ⑤✺.✾✸ ✁ ✻.✻⑤ ✏ ✵.✻✼❀ ✏ ⑤✻.✸✻ ✁ ✻.✻⑤ ✏ ✵.✷✹✳ ❉❦❤æ♥❣ t❤➼❝❤✱ t❤➼❝❤ ❉❦❤æ♥❣ t❤➼❝❤✱ r➜t t❤➼❝❤ ❉t❤➼❝❤✱ r➜t t❤➼❝❤ t❤➼❝❤✱ r➜t t❤➼❝❤ ❈❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ♥❤â♠ t❤➼❝❤ ✈➔ r➜t t❤➼❝❤ ❉ ♥❤ä ❤ì♥ ❣✐→ trà ❚ ❣✐ỵ✐ ❤↕♥✱ ♥➯♥ t❛ ❦➳t ❧✉➟♥ r➡♥❣ ♥❤â♠ s✐♥❤ ✈✐➯♥ ❝â ♠ù❝ ✤ë ②➯✉ t❤➼❝❤ ♥❣➔♥❤ ❤å❝ ♥❤✐➲✉ ❤❛② r➜t ♥❤✐➲✉ t❤➻ ❦➳t q✉↔ ❤å❝ t➟♣ ❦❤æ♥❣ ❦❤→❝ ❜✐➺t ♥❤❛✉ ✤→♥❣ ❦➸✳ ◆❤â♠ ❦❤æ♥❣ t❤➼❝❤ ♥❣➔♥❤ ❤å❝ ❝â ❦➳t q✉↔ ❤å❝ t➟♣ ❦➨♠ ❤ì♥ ❤➥♥ ❤❛✐ ♥❤â♠ t❤➼❝❤ ✈➔ r➜t t❤➼❝❤ ♥❣➔♥❤ ✤❛♥❣ ❤å❝✳ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✻ ✴ ✻✻✹ ❱➼ ❞ö ❙♦ s→♥❤ ❣✐ú❛ ❝→❝ ♥❤â♠ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐ ✭♠ù❝ ✤ë ②➯✉ t❤➼❝❤ ♥❣➔♥❤ ❤å❝✮✱ ❣✐→ trà tỵ✐ ❤↕♥✿ ❚ ✏ ✸.✵✹ ❝ ✵.✶✷✽ ✷✶ ✏ ✵.✷✻✺✳ ❚r✉♥❣ ❜➻♥❤ ❦❤è✐ ❧➛♥ ❧÷đt ❧➔✿ ✺.✾✸, ✻.✸✻, ✻.✻ ✈➔ ❝❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ❝→❝ ❦❤è✐ ❧➔ ✏ ⑤✺.✾✸ ✁ ✻.✸✻⑤ ✏ ✵.✹✸❀ ✏ ⑤✺.✾✸ ✁ ✻.✻⑤ ✏ ✵.✻✼❀ ✏ ⑤✻.✸✻ ✁ ✻.✻⑤ ✏ ✵.✷✹✳ ❉❦❤æ♥❣ t❤➼❝❤✱ t❤➼❝❤ ❉❦❤æ♥❣ t❤➼❝❤✱ r➜t t❤➼❝❤ ❉t❤➼❝❤✱ r➜t t❤➼❝❤ t❤➼❝❤✱ r➜t t❤➼❝❤ ❈❤➯♥❤ ❧➺❝❤ ❣✐ú❛ ♥❤â♠ t❤➼❝❤ ✈➔ r➜t t❤➼❝❤ ❉ ♥❤ä ❤ì♥ ❣✐→ trà ❚ ❣✐ỵ✐ ❤↕♥✱ ♥➯♥ t❛ ❦➳t ❧✉➟♥ r➡♥❣ ♥❤â♠ s✐♥❤ ✈✐➯♥ ❝â ♠ù❝ ✤ë ②➯✉ t❤➼❝❤ ♥❣➔♥❤ ❤å❝ ♥❤✐➲✉ ❤❛② r➜t ♥❤✐➲✉ t❤➻ ❦➳t q✉↔ ❤å❝ t➟♣ ❦❤æ♥❣ ❦❤→❝ ❜✐➺t ♥❤❛✉ ✤→♥❣ ❦➸✳ ◆❤â♠ ❦❤æ♥❣ t❤➼❝❤ ♥❣➔♥❤ ❤å❝ ❝â ❦➳t q✉↔ ❤å❝ t➟♣ ❦➨♠ ❤ì♥ ❤➥♥ ❤❛✐ ♥❤â♠ t❤➼❝❤ ✈➔ r➜t t❤➼❝❤ ♥❣➔♥❤ ✤❛♥❣ ❤å❝✳ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✻ ✴ ✻✻✹ ❚❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘ ❚❛ ❞ò♥❣ ❤➔♠ ❚✉❦❡②❍❙❉✭✮ ✤➸ t❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘✳ ❈❤➥♥❣ ❤↕♥✱ tr♦♥❣ ✈➼ ❞ö tr➯♥ t❛ ❝❤➾ ❝➛♥ t❤ü❝ ❤✐➺♥✿ ❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐✮✮ ❚❛ ❝â t❤➸ ♠✐♥❤ ❤å❛ sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❝→❝ tr✉♥❣ ❜➻♥❤ ♥➔② ❜➡♥❣ ❧➺♥❤ ♣❧♦t✭❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠✮✮✮ ♣❧♦t✭❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥❑❤♦✐✮✮✮ ✣➸ ♠✐♥❤ ❤å❛ sü t÷ì♥❣ t→❝ ❣✐ú❛ ❝→❝ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ✤➳♥ ②➳✉ tè ❦➳t q✉↔✱ t❛ ❞ị♥❣ ❤➔♠ ✐♥t❡r❛❝t✐♦♥✳♣❧♦t ✐♥t❡r❛❝t✐♦♥✳♣❧♦t✭P❤❛♥◆❤♦♠✱ P❤❛♥❑❤♦✐✱ ▼❛✉●♦♣✮ ❇ë ♠ỉ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✼ ✴ ✻✻✹ ❚❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘ ❚❛ ❞ò♥❣ ❤➔♠ ❚✉❦❡②❍❙❉✭✮ ✤➸ t❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘✳ ❈❤➥♥❣ ❤↕♥✱ tr♦♥❣ ✈➼ ❞ö tr➯♥ t❛ ❝❤➾ ❝➛♥ t❤ü❝ ❤✐➺♥✿ ❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐✮✮ ❚❛ ❝â t❤➸ ♠✐♥❤ ❤å❛ sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❝→❝ tr✉♥❣ ❜➻♥❤ ♥➔② ❜➡♥❣ ❧➺♥❤ ♣❧♦t✭❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠✮✮✮ ♣❧♦t✭❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥❑❤♦✐✮✮✮ ✣➸ ♠✐♥❤ ❤å❛ sü t÷ì♥❣ t→❝ ❣✐ú❛ ❝→❝ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ✤➳♥ ②➳✉ tè ❦➳t q✉↔✱ t❛ ❞ò♥❣ ❤➔♠ ✐♥t❡r❛❝t✐♦♥✳♣❧♦t ✐♥t❡r❛❝t✐♦♥✳♣❧♦t✭P❤❛♥◆❤♦♠✱ P❤❛♥❑❤♦✐✱ ▼❛✉●♦♣✮ ❇ë ♠æ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✼ ✴ ✻✻✹ ❚❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘ ❚❛ ❞ò♥❣ ❤➔♠ ❚✉❦❡②❍❙❉✭✮ ✤➸ t❤ü❝ ❤✐➺♥ ♣❤➙♥ t➼❝❤ s➙✉ ❚✇♦✲✇❛② ❆◆❖❱❆ tr♦♥❣ ❘✳ ❈❤➥♥❣ ❤↕♥✱ tr♦♥❣ ✈➼ ❞ö tr➯♥ t❛ ❝❤➾ ❝➛♥ t❤ü❝ ❤✐➺♥✿ ❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠ ✰ P❤❛♥❑❤♦✐✮✮ ❚❛ ❝â t❤➸ ♠✐♥❤ ❤å❛ sü ❦❤→❝ ❜✐➺t ❣✐ú❛ ❝→❝ tr✉♥❣ ❜➻♥❤ ♥➔② ❜➡♥❣ ❧➺♥❤ ♣❧♦t✭❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥◆❤♦♠✮✮✮ ♣❧♦t✭❚✉❦❡②❍❙❉✭❛♦✈✭▼❛✉●♦♣ ∼ P❤❛♥❑❤♦✐✮✮✮ ✣➸ ♠✐♥❤ ❤å❛ sü t÷ì♥❣ t→❝ ❣✐ú❛ ❝→❝ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ ✤➳♥ ②➳✉ tè ❦➳t q✉↔✱ t❛ ❞ị♥❣ ❤➔♠ ✐♥t❡r❛❝t✐♦♥✳♣❧♦t ✐♥t❡r❛❝t✐♦♥✳♣❧♦t✭P❤❛♥◆❤♦♠✱ P❤❛♥❑❤♦✐✱ ▼❛✉●♦♣✮ ❇ë ♠ỉ♥ ❚❖⑩◆ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ù♥❣ ❞ö♥❣ ◆❣➔② ✶✹ t❤→♥❣ ✷ ♥➠♠ ✷✵✵✾ ✹✾✼ ✴ ✻✻✹

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