Bài giảng xác suất thống kê và ứng dụng phần 4 phan thanh hồng 1

❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ P❤❛♥ ỗ ổ t P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✶ ✴ ✺✶ P❤➛♥ ■❱ ữủ tố ổ t P ỗ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✷ ✴ ✺✶ P❤➛♥ ■❱ ✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✷ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë ♣❤➙♥ t→♥ ✸ P❤➙♥ ✈à✱ tù ♣❤➙♥ ✈à✱ ✤ë tr ỳ ỗ r ỷ ❦➳t ❤ñ♣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ P❤➛♥ ■❱ ✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✷ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë ♣❤➙♥ t→♥ ✸ P❤➙♥ ✈à✱ tù ♣❤➙♥ ✈à✱ tr ỳ ỗ r ỷ ❞ư♥❣ ❦➳t ❤đ♣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ P❤❛♥ ỗ st ố ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ P❤➛♥ ■❱ ✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✷ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠æ t↔ ✤ë ♣❤➙♥ t→♥ ✸ P❤➙♥ ✈à✱ tù ♣❤➙♥ tr ỳ ỗ r ❙û ❞ư♥❣ ❦➳t ❤đ♣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ P ỗ st ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ P❤➛♥ ■❱ ✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠æ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✷ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë ♣❤➙♥ t→♥ ✸ P❤➙♥ ✈à✱ tù tr ỳ ỗ r ✹ ❙û ❞ư♥❣ ❦➳t ❤đ♣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ t❤è♥❣ ❦➯ ♠ỉ t↔ P❤➛♥ ♥➔② tr➻♥❤ ❜➔② ✈➲ ❝→❝ ✤↕✐ ❧÷đ♥❣ t❤è♥❣ ❦➯ ♠æ t↔ ❝õ❛ ♠ët tê♥❣ t❤➸ ❝→❝ q✉❛♥ s→t ✈➔ ♠➝✉ ♥❤ú♥❣ q✉❛♥ s→t ✤÷đ❝ rót r❛ ♠ët ❝→❝❤ ♥❣➝✉ ♥❤✐➯♥ tø ♠ët tê♥❣ t❤➸✳ ❱➔ ✈➻ ♣❤➛♥ ợ trữớ ủ t õ õ t t t ❝→❝ ✤↕✐ ❧÷đ♥❣ ♥➔② ❝❤♦ t➟♣ ❞ú ❧✐➺✉ tê♥❣ t❤➸ ♥➯♥ ❝❤õ ②➳✉ t❛ ❧➔♠ ✈✐➺❝ ✈ỵ✐ ❝→❝ ♠➝✉ ✈➔ ũ t t tr ữợ ữủ tê♥❣ t❤➸✳ P❤➛♥ ♥➔② ❝ô♥❣ s➩ tr➻♥❤ ❜➔② ❝→❝❤ t➼♥❤ ❝→❝ ✤↕✐ ❧÷đ♥❣ t❤è♥❣ ❦➯ ♠ỉ t↔ ❝❤♦ ❤❛✐ tr÷í♥❣ ❤ñ♣ t➟♣ ❞ú ❧✐➺✉ ♠➝✉ ❣è❝ ✈➔ t➟♣ ❞ú ❧✐➺✉ ♠➝✉ ✤➣ ✤÷đ❝ tâ♠ t➢t tr♦♥❣ ❜↔♥❣ t➛♥ sè✳ P❤❛♥ ỗ st ố ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹ ✴ ✺✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✶ ✷ ✸ ❚r✉♥❣ ❜➻♥❤ ❚r✉♥❣ ✈à P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✺ ✴ ✺✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠ỉ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✶ ✷ ✸ ❚r✉♥❣ ❜➻♥❤ r P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✺ ✴ ✺✶ ❈→❝ ✤↕✐ ❧÷đ♥❣ ♠æ t↔ ✤ë t➟♣ tr✉♥❣ ✭tr✉♥❣ t➙♠✮ ✶ ✷ ✸ r r P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✺ ✴ ✺✶ ❇✐➸✉ ỗ r t ỗ ✈➔ r➙✉ ❜✐➸✉ ❞✐➵♥ ✺ sè ✤♦✿ ❣✐→ trà ♥❤ä ♥❤➜t✱ ❣✐→ trà ❧ỵ♥ ♥❤➜t ✈➔ ❝→❝ tù ♣❤➙♥ ✈à t❤ù ♥❤➜t✱ t❤ù ❤❛✐✱ t❤ù ❜❛✳ ❍ë♣ ❤➻♥❤ ❝❤ú ♥❤➟t t❤➸ ❤✐➺♥ ✺✵% ❝→❝ q✉❛♥ s→t ð ❣✐ú❛ t➟♣ ❞ú ❧✐➺✉✱ ❝❤✐➲✉ rë♥❣ ❝õ❛ ❤ë♣ ❜➡♥❣ ✤ë tr↔✐ ❣✐ú❛ ❘◗ ✱ ❤❛✐ ❝↕♥❤ ❜➯♥ ✤✐ q✉❛ ❣✐→ trà tù ♣❤➙♥ ✈à t❤ù ♥❤➜t ✈➔ t❤ù ❜❛✳ ✣÷í♥❣ t❤➥♥❣ ✤ù♥❣ ❜➯♥ tr♦♥❣ ❤ë♣ ✤✐ q✉❛ ❣✐→ trà tù ♣❤➙♥ ✈à t❤ù r ỗ % q st ữợ % q st tr ◗✸ ✳ ❘➙✉ tr→✐ ✤✐ tø ◗✶ ✤➳♥ ❣✐→ trà ♥❤ä ♥❤➜t✱ r➙✉ ♣❤↔✐ ✤✐ tø ◗✸ ✤➳♥ ❣✐→ trà ợ t ỗ t ❝→✐ ♥❤➻♥ tê♥❣ q✉→t ✈➲ sü ♣❤➙♥ t→♥ ❝õ❛ t➟♣ ❞ú ❧✐➺✉ ✷ ❈❤♦ ❜✐➳t t➼♥❤ ❝❤➜t ✤é✐ ①ù♥❣ ❤❛② ♥❣❤✐➯♥❣ ❝õ❛ t➟♣ ❞ú ❧✐➺✉ ✸ ❈❤♦ ❜✐➳t ❝→❝ ❣✐→ trà ♥❣♦↕✐ ❜✐➯♥✳ ✹ ❉➵ ❞➔♥❣ s♦ s→♥❤ ♥❤✐➲✉ t➟♣ ỳ ỗ P ỗ st ố ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ỗ r t ỗ r số ✤♦✿ ❣✐→ trà ♥❤ä ♥❤➜t✱ ❣✐→ trà ❧ỵ♥ ♥❤➜t ✈➔ ❝→❝ tù ♣❤➙♥ ✈à t❤ù ♥❤➜t✱ t❤ù ❤❛✐✱ t❤ù ❜❛✳ ❍ë♣ ❤➻♥❤ ❝❤ú ♥❤➟t t❤➸ ❤✐➺♥ ✺✵% ❝→❝ q✉❛♥ s→t ð ❣✐ú❛ t➟♣ ❞ú ❧✐➺✉✱ ❝❤✐➲✉ rë♥❣ ❝õ❛ ❤ë♣ ❜➡♥❣ ✤ë tr↔✐ ❣✐ú❛ ❘◗ ✱ ❤❛✐ ❝↕♥❤ ❜➯♥ ✤✐ q✉❛ ❣✐→ trà tù ♣❤➙♥ ✈à t❤ù ♥❤➜t ✈➔ t❤ù ❜❛✳ ✣÷í♥❣ t❤➥♥❣ ✤ù♥❣ ❜➯♥ tr♦♥❣ ❤ë♣ ✤✐ q✉❛ ❣✐→ trà tự tự r ỗ % q st ữợ % q✉❛♥ s→t ♣❤➼❛ tr➯♥ ◗✸ ✳ ❘➙✉ tr→✐ ✤✐ tø ◗✶ ✤➳♥ ❣✐→ trà ♥❤ä ♥❤➜t✱ r➙✉ ♣❤↔✐ ✤✐ tø ◗✸ ✤➳♥ ❣✐→ trà ❧ỵ♥ ♥❤➜t✳ ❚→❝ ❞ư♥❣ ❝õ❛ ❜✐➸✉ ỗ t tờ qt sỹ ♣❤➙♥ t→♥ ❝õ❛ t➟♣ ❞ú ❧✐➺✉ ✷ ❈❤♦ ❜✐➳t t➼♥❤ ❝❤➜t ✤é✐ ①ù♥❣ ❤❛② ♥❣❤✐➯♥❣ ❝õ❛ t➟♣ ❞ú ❧✐➺✉ ✸ ❈❤♦ ❜✐➳t ❝→❝ ❣✐→ trà ♥❣♦↕✐ ❜✐➯♥✳ ✹ ❉➵ ❞➔♥❣ s♦ s→♥❤ ♥❤✐➲✉ t➟♣ ❞ú ❧✐➺✉ ❦❤✐ ✈➩ ❝→❝ ❜✐➸✉ ỗ P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✵ ✴ ✺✶ ❙û ❞ö♥❣ ❦➳t ❤ñ♣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ ✶ ✷ ✸ ✹ ❍➺ sè ❜✐➳♥ t❤✐➯♥ ◗✉② t➢❝ t❤ü❝ ♥❣❤✐➺♠ ◗✉② t s õ ỳ P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✶ ✴ ✺✶ ❍➺ sè ❜✐➳♥ t❤✐➯♥ ✣➸ ✤♦ ❧÷í♥❣ ♠ù❝ ✤ë ❜✐➳♥ ✤ë♥❣ t÷ì♥❣ ✤è✐ ❝õ❛ ♥❤ú♥❣ t➟♣ ❞ú ❧✐➺✉ ❝â ❣✐→ trà tr✉♥❣ ❜➻♥❤ ❦❤→❝ ♥❤❛✉ ♥❣÷í✐ t❛ sû ❞ư♥❣ ❤➺ sè ❜✐➳♥ t❤✐➯♥✳ ❍➺ sè ❜✐➳♥ t❤✐➯♥ ❝õ❛ ♠ët tê♥❣ t❤➸ ❝→❝ q✉❛♥ s→t✿ ❈❱ ✏ ✁σ ✠ µ ☎ ✶✵✵% ❍➺ sè ❜✐➳♥ t❤✐➯♥ ❝õ❛ ♠ët ♠➝✉ ♥❤ú♥❣ q✉❛♥ s→t✿ ✁ ✠ ❈❱ ✏ ①s ☎ ✶✵✵% ❑❤✐ s♦ s→♥❤ ❤❛✐ t➟♣ ❞ú ❧✐➺✉✱ t➟♣ ❞ú ❧✐➺✉ ♥➔♦ ❝â ❤➺ sè ❜✐➳♥ t❤✐➯♥ ❧ỵ♥ ❤ì♥ t❤➻ ❜✐➳♥ ✤ë♥❣ ♥❤✐➲✉ ỡ P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✷ ✴ ✺✶ ◗✉② t➢❝ t❤ü❝ ♥❣❤✐➺♠ ◆➳✉ ♠ët tê♥❣ t❤➸ ❝â tr✉♥❣ ❜➻♥❤ µ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ σ ♠➔ ♣❤➙♥ ♣❤è✐ ❝â ❞↕♥❣ ❤➻♥❤ ❝❤✉æ♥❣ ❝➙♥ ✤è✐ t❤➻ ❑❤♦↔♥❣ ✻✽% sè q✉❛♥ s→t ❝õ❛ tê♥❣ t❤➸ t❤✉ë❝ ✈➔♦ ❦❤♦↔♥❣ rµ ✁ σ, µ   σs✳ ❑❤♦↔♥❣ ✾✺% sè q✉❛♥ s→t ❝õ❛ tê♥❣ t❤➸ t❤✉ë❝ ✈➔♦ ❦❤♦↔♥❣ rµ ✁ ✷σ, µ   ✷σs✳ ❑❤♦↔♥❣ ✾✾.✼% sè q✉❛♥ s→t ❝õ❛ tê♥❣ t❤➸ t❤✉ë❝ ✈➔♦ ❦❤♦↔♥❣ rµ ✁ ✸σ, s P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✸ ✴ ✺✶ ◗✉② t➢❝ t❤ü❝ ♥❣❤✐➺♠ 68% µ−σ 95% µ+σ µ − 2σ σ 99.7% µ + 2σ σ µ − 3σ σ P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ Ù♥❣ ❞ư♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ µ + 3σ σ ✹✹ ✴ ✺✶ ◗✉② t➢❝ t❤ü❝ ♥❣❤✐➺♠ ❳➨t ♠➝✉ ✹✾ ❧÷đ♥❣ ①➠♥❣ t✐➯✉ t❤ư tr♦♥❣ ♣❤➛♥ ■■■✱ ❜✐➸✉ ❞✐➵♥ t❤➙♥ ✈➔ ❧→ ❝õ❛ t➟♣ ❞ú ❧✐➺✉ ♥➔② ❝❤♦ t❤➜② ♣❤➙♥ ♣❤è✐ ❝õ❛ ♠➝✉ ❝â ❞↕♥❣ ❤➻♥❤ ❝❤✉æ♥❣ ❝➙♥ ✤è✐✳ ✷✾ ✸✵ ✸✵ ✸✶ ✸✶ ✸✷ ✸✷ ✸✸ ✽ ✶✸✹✹ ✺✻✻✻✽✽✾ ✵✵✶✷✸✸✹✹✹ ✺✺✺✻✻✼✼✼✽✽✾ ✵✵✵✶✶✷✷✸✹✹ ✺✺✻✼✽✽ ✸ P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✺ ✴ ✺✶ ◗✉② t➢❝ t❤ü❝ ♥❣❤✐➺♠ ❚❛ t➼♥❤ ✤÷đ❝ ① ✏ ✸✶.✺✺✸✶ ✈➔ s ✏ ✵.✼✾✾✷✳ ❚❛ ❧➜② ❤❛✐ ❣✐→ tr ữợ ữủ tr ❝❤✉➞♥ tê♥❣ t❤➸ ❝→❝ ❧÷đ♥❣ ①➠♥❣ t✐➯✉ t❤ư tr➯♥ ✺✵✵ ❦♠✳ ⑩♣ ❞ö♥❣ q✉② t➢❝ t❤ü❝ ♥❣❤✐➺♠ t❛ ❝â✿ ✶ r① ✁ s , ①   s s ✏ r✸✵.✽, .s t ữợ ữủ r % số t t❤ö tø ✸✵✳✽ ✤➳♥ ✸✷✳✹ ❧➼t ①➠♥❣ tr➯♥ ✺✵✵ ❦♠✳ ✷ r① ✁ ✷s , ①   ✷s s ✏ r., .s t ữợ ữủ r % số t✐➯✉ t❤ö tø ✸✵✳✵ ✤➳♥ ✸✸✳✷ ❧➼t ①➠♥❣ tr➯♥ ✺✵✵ ❦♠✳ ✸ r① ✁ ✸s , ①   ✸s s r., .s t ữợ ữủ r .% số ①❡ t✐➯✉ t❤ö tø ✷✾✳✷ ✤➳♥ ✸✹ ❧➼t ①➠♥❣ tr➯♥ P ỗ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✻ ✴ ✺✶ ◗✉② t➢❝ ❈❤❡❜②s❤❡✈ ✣à♥❤ ỵ s t ởt tờ t õ tr ợ sè ❦ → ✶✱ ➼t ♥❤➜t ✶✵✵♣✶ ✁ ✶④❦ ✷ q% sè ❝→❝ q✉❛♥ s→t ♥➡♠ tr♦♥❣ ❦❤♦↔♥❣ rµ ✁ , s P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✼ ✴ ✺✶ ❈❤✉➞♥ ❤â❛ ❞ú ❧✐➺✉ ❚❛ ❝â t❤➸ ①→❝ ✤à♥❤ ✈à tr➼ t÷ì♥❣ ✤è✐ ❝õ❛ ♠ët ❣✐→ trà tr♦♥❣ tê♥❣ t❤➸ ❤❛② ♠➝✉ ❜➡♥❣ ❝→❝❤ sû ❞ö♥❣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ ✤➸ t➼♥❤ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③✳ ❈❤♦ ① ❧➔ ♠ët ❣✐→ trà tr♦♥❣ tê♥❣ t❤➸ ❤❛② ♠➝✉✱ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ✤÷ì❝ t➼♥❤ ♥❤÷ s❛✉ ③ ✏ ① ✁ tr✉♥❣ ❜➻♥❤ ✤ë ❧➺❝❤ ❝❤✉➞♥ ③ ❝á♥ ✤÷đ❝ ❣å✐ ❧➔ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ❝õ❛ ①✳ ◆➳✉ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ❧➔ ✸✳✶ t❤➻ ① ❧ỵ♥ ❤ì♥ ✸✳✶ ❧➛♥ ✤ë ❧➺❝❤ ❝❤✉➞♥ s♦ ✈ỵ✐ tr✉♥❣ ❜➻♥❤✳ ◆➳✉ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ❧➔ ✲✶✳✼ t❤➻ ① ♥❤ä ❤ì♥ ✶✳✼ ❧➛♥ s ợ tr P ỗ ✭✣❍ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✽ ✴ ✺✶ ❈❤✉➞♥ ❤â❛ ❞ú ❧✐➺✉ ❚❛ ❝â t❤➸ ①→❝ ✤à♥❤ ✈à tr➼ t÷ì♥❣ ✤è✐ ❝õ❛ ♠ët ❣✐→ trà tr♦♥❣ tê♥❣ t❤➸ ❤❛② ♠➝✉ ❜➡♥❣ ❝→❝❤ sû ❞ö♥❣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ ✤➸ t➼♥❤ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③✳ ❈❤♦ ① ❧➔ ♠ët ❣✐→ trà tr♦♥❣ tê♥❣ t❤➸ ❤❛② ♠➝✉✱ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ✤÷ì❝ t➼♥❤ ♥❤÷ s❛✉ ③ ✏ ① ✁ tr✉♥❣ ❜➻♥❤ ✤ë ❧➺❝❤ ❝❤✉➞♥ ③ ❝á♥ ✤÷đ❝ ❣å✐ ❧➔ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ❝õ❛ ①✳ ◆➳✉ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ❧➔ ✸✳✶ t❤➻ ① ❧ỵ♥ ❤ì♥ ✸✳✶ ❧➛♥ ✤ë ❧➺❝❤ ❝❤✉➞♥ s♦ ✈ỵ✐ tr✉♥❣ ❜➻♥❤✳ ◆➳✉ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ❧➔ ✲✶✳✼ t❤➻ ① ♥❤ä ❤ì♥ ✶✳✼ ❧➛♥ ✤ë ❧➺❝❤ ❝❤✉➞♥ s♦ ✈ỵ✐ tr✉♥❣ ❜➻♥❤✳ P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✽ ✴ ✺✶ ❈❤✉➞♥ ❤â❛ ❞ú ❧✐➺✉ ❚❛ ❝â t❤➸ ①→❝ ✤à♥❤ ✈à tr➼ t÷ì♥❣ ✤è✐ ❝õ❛ ♠ët ❣✐→ trà tr♦♥❣ tê♥❣ t❤➸ ❤❛② ♠➝✉ ❜➡♥❣ ❝→❝❤ sû ❞ö♥❣ tr✉♥❣ ❜➻♥❤ ✈➔ ✤ë ❧➺❝❤ ❝❤✉➞♥ ✤➸ t➼♥❤ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③✳ ❈❤♦ ① ❧➔ ♠ët ❣✐→ trà tr♦♥❣ tê♥❣ t❤➸ ❤❛② ♠➝✉✱ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ✤÷ì❝ t➼♥❤ ♥❤÷ s❛✉ ③ ✏ ① ✁ tr✉♥❣ ❜➻♥❤ ✤ë ❧➺❝❤ ❝❤✉➞♥ ③ ❝á♥ ✤÷đ❝ ❣å✐ ❧➔ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ❝õ❛ ①✳ ◆➳✉ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ❧➔ ✸✳✶ t❤➻ ① ❧ỵ♥ ❤ì♥ ✸✳✶ ❧➛♥ ✤ë ❧➺❝❤ ❝❤✉➞♥ s♦ ✈ỵ✐ tr✉♥❣ ❜➻♥❤✳ ◆➳✉ ❣✐→ trà ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ① ❧➔ ✲✶✳✼ t❤➻ ① ♥❤ä ❤ì♥ ✶✳✼ ❧➛♥ ✤ë ❧➺❝❤ ❝❤✉➞♥ s♦ ✈ỵ✐ tr✉♥❣ ❜➻♥❤✳ P❤❛♥ ỗ st ố ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✽ ✴ ✺✶ ❈❤✉➞♥ ❤â❛ ❞ú ❧✐➺✉ ❱➼ ❞ö✿ ❳➨t ✤✐➸♠ t❤✐ ♠æ♥ t❤è♥❣ ❦➯ ❝õ❛ ❤❛✐ ♥❤â♠ s✐♥❤ ✈✐➯♥✳ ◆❤â♠ ✶ ❝â tr✉♥❣ ❜➻♥❤ ✻✺✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ✶✵✳ ◆❤â♠ ✷ ❝â tr✉♥❣ ❜➻♥❤ ✽✵✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ✺✳ ▼ët s✐♥❤ ✈✐➯♥ ♥❤â♠ ✶ ❝â ✤✐➸♠ t❤✐ ❧➔ ✽✺✱ ✈➔ ♠ët s✐♥❤ ✈✐➯♥ ♥❤â♠ ✷ ❝â ✤✐➸♠ t❤✐ ❧➔ ✾✵ s➩ ❝â ✈à tr➼ t÷ì♥❣ ✤è✐ tr♦♥❣ ♥❤â♠ ❝õ❛ ♠➻♥❤ ♥❤÷ ♥❤❛✉ ✈➻ ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ✽✺ ❧➔ ③✶ ✏ ♣✽✺ ✁ ✻✺q④✶✵ ✏ ✷ ✈➔ ❝❤✉➞♥ ❤â❛ ③ ❝õ❛ ✾✵ ❧➔ ③✷ ✏ ♣✾✵ ✁ ✽✵q④✺ ✏ P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✹✾ ✴ ✺✶ ❚➼♥❤ ❝→❝ ✤↕✐ ❧÷đ♥❣ t❤è♥❣ ❦➯ ♠æ t↔ tr♦♥❣ ❘ ♠❡❛♥✭①✱ tr✐♠ ❂ ✵✱ ♥❛✳r♠ ❂ ❋❆▲❙❊✱ ✳✳✳✮ ♠❡❞✐❛♥✭①✱ ♥❛✳r♠ ❂ ❋❆▲❙❊✮ r❛♥❣❡✭①✱ ♥❛✳r♠ ❂ ❋❆▲❙❊✮ ✈❛r✭①✱ ♥❛✳r♠ ❂ ❋❆▲❙❊✮ s❞✭①✱ ♥❛✳r♠ ❂ ❋❆▲❙❊✮ q✉❛♥t✐❧❡✭①✱ ♣r♦❜s ❂ s❡q✭✵✱ ✶✱ ✵✳✷✺✮✱ ♥❛✳r♠ ❂ ❋❆▲❙❊✱✳✳✳✮ ❢✐✈❡♥✉♠✭①✱ ♥❛✳r♠ ❂ ❚❘❯❊✮ s✉♠♠❛r②✭①✮ ❜♦①♣❧♦t✭①✱❤♦r✐③♦♥t❛❧❂❋❆▲❙❊✱✳✳✳✮ ❚r✉♥❣ ❜➻♥❤ ❚r✉♥❣ ✈à ❑❤♦↔♥❣ ❜✐➳♥ t❤✐➯♥ P❤÷ì♥❣ s❛✐ ♠➝✉ ✣ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ P❤➙♥ ✈à ỗ r P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✺✵ ✴ ✺✶ ❚➼♥❤ ❝→❝ ✤↕✐ ❧÷đ♥❣ t❤è♥❣ ❦➯ ♠ỉ t↔ tr♦♥❣ ❘ ❚r♦♥❣ ✤â ①✿ t➟♣ ❞ú ❧✐➺✉ ♥❛✳r♠✿ t❤❛♠ sè ❧♦❣✐❝ ❋❆▲❙❊✴❚❘❯❊ ❦❤æ♥❣ ❜ä q✉❛✴❜ä q✉❛ ♥❤ú♥❣ ❣✐→ trà trè♥❣ ❦❤æ♥❣ tr♦♥❣ q tr t t P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✵✾ ✺✶ ✴ ✺✶ ... t❤→♥❣ ✶✶ ♥➠♠ ỗ r t ỗ r ♠➝✉ ✻✺ t❤í✐ ❣✐❛♥ t❤❛♥❤ t♦→♥ Bieu hop va rau cua mau 65 tgtt 10 15 20 25 30 P ỗ st ❚❤è♥❣ ❦➯ ✈➔ Ù♥❣ ❞ö♥❣ ◆❣➔② ✷✶ t❤→♥❣ ✶✶ ♥➠♠ ỗ r t ỗ r sè