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ຊ౰ͷ౷ܭֶɾ֬཰ೖ໳ Ya8 2024@ίίωϦϗʔϧ 2024/3/15 by kataokatsuki @kataokatsuki 1

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ࣗݾ঺հ — Kataoka Katsuki — id: kataokatsuki — ໊ݹ԰ͷελʔτΞοϓ Sonoligo Ͱಇ͍ͯ·͢ — RubyΛΑ͘ॻ͖·͢ — झຯͰ౷ܭֶΛษڧͯ͠·͢ @kataokatsuki 2

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͜ͷτʔΫͷΰʔϧ ౷ܭֶΛษڧͨͯ͠ͷࠒʹग़ͯ͘Δ֓೦Λ ݱ࣮ͷͰ͖͝ͱͱ݁ͼ͚ͭͯཧղ͢Δ͜ͱ ·ͣ͸ਖ਼͠͞ΑΓ ʮԿΛݴ͍ͬͯΔͷ͔ʁʯΛΠϝʔδ Ͱ͖ΔΑ͏ʹ͢Δ @kataokatsuki 3

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ @kataokatsuki 4

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෼໺ɾख๏౳ͷؔ܎ੑ @kataokatsuki 5

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౷ܭֶͷ֓ཁ @kataokatsuki 6

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ @kataokatsuki 7

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໰୊ — ೔ຊਓͷฏۉ਎௕͸Կcmʁ @kataokatsuki 8

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ʮղ͖ํʯʹண໨ @kataokatsuki 9

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શମΛݟΔ͔ɺҰ෦ΛݟͯશମΛਪଌ͢Δ͔ — ೔ຊਓશମΛଌΔ هड़౷ܭֶ (શମΛߟ࡯͢Δ) — ͋Δఔ౓ͷਓ਺Λଌͬͯɺ͔ͦ͜Β೔ຊਓશମΛਪଌ͢Δ ਪଌ౷ܭֶ (Ұ෦͔ΒɺશମΛਪଌ͢Δ) @kataokatsuki 10

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໰୊ 100໊ͷσʔλ͕༩͑ΒΕΔʢҰ෦͔ΒɺશମΛਪଌ͢Δʣ — ೔ຊਓͷฏۉ਎௕͸Կcmʁ — ͋ΔӡಈϓϩάϥϜ͸೔ຊਓͷ਎௕Λߴ͘͢Δ͔ʁ @kataokatsuki 11

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ʮղʯʹண໨ @kataokatsuki 12

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਺஋͔ɺਅِ஋͔ — ೔ຊਓͷฏۉ਎௕͸Կcmʁ ਪఆ (~cmͳͲͷ਺஋ΛಘΔ) — ͋ΔӡಈϓϩάϥϜ͸਎௕ʹྑ͍ӨڹΛ༩͑Δ͔ʁ ݕఆ (Yes/Noͷਅِ஋ΛಘΔ) @kataokatsuki 13

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هड़౷ܭֶ @kataokatsuki 14

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ @kataokatsuki 15

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ಘΒΕͨσʔλࣗମΛ෼ੳ͢Δ @kataokatsuki 16

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@kataokatsuki 17

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1. ਤͳͲͰදه͠ɺσʔλΛࢹ֮తʹଊ͑΍͘͢͢Δ — ౓਺෼෍දɾώετάϥϜɾശͻ͛ਤɾࢄ෍ਤͳͲ 2. σʔλͷಛੑΛද͢஋Λࢉग़͢Δ — ฏۉɾதԝ஋ɾ࠷ස஋ɾ෼ࢄɾඪ४ภࠩͳͲ @kataokatsuki 18

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ਤͳͲͰදه͠ɺࢹ֮తʹଊ͑΍͘͢͢Δ — ౓਺෼෍දɾώετάϥϜ — ശͻ͛ਤ — ࢄ෍ਤ — ંΕઢάϥϑ — ԁάϥϑ — ๮άϥϑ — ύϨʔτਤ — υοτϓϩοτ — ώʔτϚοϓ @kataokatsuki 19

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σʔλશମͷಛੑΛද͢஋Λࢉग़͢Δ — ฏۉ: Mean — தԝ஋: Median — ࠷ස஋: Mode — ෼ࢄ: Variance — ඪ४ภࠩ: Standard Deviation — ൣғ: Range — 25%ύʔηϯλΠϧ: 25th Percentile — 50%ύʔηϯλΠϧ (தԝ஋): 50th Percentile — 75%ύʔηϯλΠϧ: 75th Percentile — ࿪౓: Skewness — ઑ౓: Kurtosis @kataokatsuki 20

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ਪଌ౷ܭֶ @kataokatsuki 21

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ @kataokatsuki 22

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ಘΒΕͨσʔλ͔Β എޙʹ͋Δ࢓૊ΈΛਪଌ͢Δ @kataokatsuki 23

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@kataokatsuki 24

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ू߹࿦ @kataokatsuki 25

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ @kataokatsuki 26

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ू߹ͱݩ1 ू߹ɾɾݩͷू·Γ ݩɾɾࢥߟͱର৅ͱͳΔݸʑͷʮ΋ͷʯʢू߹ͷߏ੒ཁૉʣ ू߹ͷදݱ͸2௨Γ͋Δ 1. ֎Ԇతه๏ ݩ, ݩ, 2. ಺แతه๏2 ม਺ | ม਺Λ༻໋͍ͨ୊ 2 ໋୊ɾɾਅ (true) Ͱ͋Δِ͔ (false) Ͱ͋Δ͔͕͸͖ͬΓͱ͍ͯ͠Δࣄ 1 https://www.math.is.tohoku.ac.jp/~oC2ata/student/subject/file/2018-2_shugo.pdf @kataokatsuki 27

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ྫ 1Ҏ্5ҎԼͷࣗવ਺͔Β੒Δू߹ 1. ֎Ԇతه๏ 元 元 2. ಺แతه๏ 変数 命題 ͸1Ҏ্5ҎԼͷࣗવ਺ # ಺แతه๏ͷΠϝʔδ A = (1..10000).select { |a| a if 0 <= a && a <= 5 } = [1, 2, 3, 4, 5] @kataokatsuki 28

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֬཰࿦ @kataokatsuki 29

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 30

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ࣄ৅ͱू߹/݁Ռͱݩ @kataokatsuki 31

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 32

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͍͜͞ΖΛ1ͭ౤͛Δ࣌ ى͜Γ͏Δঢ়ଶʢࣄ৅ͱݺͿʣ͸ͲΕʁ 1. 1ͷ໨͕ग़ͨ 2. ۮ਺ͷ໨͕ग़ͨ 3. 1Ҏ্3ҎԼͷ໨͕ग़ͨ 4. 7ͷ໨͕ग़ͨ @kataokatsuki 33

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1~3͸ࣄ৅ͱͯ͠ى͜Γ͏Δ 1. 1ͷ໨͕ग़ͨ 2. ۮ਺ͷ໨͕ग़ͨ 3. 1Ҏ্3ҎԼͷ໨͕ग़ͨ 4. 7ͷ໨͕ग़ͨ @kataokatsuki 34

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ʮࣄ৅ʯΛͲ͏ଊ͑Δʁ @kataokatsuki 35

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ࣄ৅ʢͷൃੜʣΛ ݁ՌΛݩͱ͢Δू߹ Ͱදݱ͢Δ @kataokatsuki 36

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ू߹࿦ ֬཰࿦ ू߹ ࣄ৅ ݩ ݁Ռ @kataokatsuki 37

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͍͜͞ΖΛ1ճৼΔͱग़Δ໨͕֬ఆ͢Δ ֬ఆͨ͠৘ใΛʮ݁Ռʯ(ू߹ͷݩʹ૬౰ʣͱݺͼɺ ͦΕͧΕͷ݁ՌΛ ͱද͢ — 1ͷ໨͕ग़Δɾɾ — 2ͷ໨͕ग़Δɾɾ — 3ͷ໨͕ग़Δɾɾ — 4ͷ໨͕ग़Δɾɾ — 5ͷ໨͕ग़Δɾɾ — 6ͷ໨͕ग़Δɾɾ @kataokatsuki 38

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ࣄ৅ ͷൃੜΛରԠ͢Δू߹ Ͱදݱ ྫ1 ࣄ৅ ͍͜͞ΖΛ1ճ౤͛ͯɺۮ਺ͷ໨͕ग़ͨ ू߹ 2ͷ໨͕ग़Δ, 4ͷ໨͕ग़Δ, 6ͷ໨͕ग़Δ ྫ2 ࣄ৅ ίΠϯ2ຕΛ1ճ౤͛ͯɺද͕1ຕग़ͨ ू߹ (ද, ཪ), (ཪ, ද) @kataokatsuki 39

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ू߹ͱࣄ৅Λ໌֬ʹ۠ผͤͣʹදݱ͢Δ ͋Δࣄ৅ ͕ൃੜͨ࣌͠ɺ ࣄ৅ ʹରԠ͢Δू߹ ͕ʮू߹ ʯͱදݱ͞ΕΔ৔߹ ͕ൃੜ͢Δ࣌ɺ ͷ࣌ɺ ͱ͍͏දݱΛ࢖͏ ࣄ৅ͱू߹ͱ͍͏ɺҰݟ͢Δͱผͷ֓೦͕͍ࠞͬͯ͟Δײ͕ͯࠞ͡͠ཚ͢Δ͔΋ @kataokatsuki 40

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ྫ1 ͕ൃੜͨ࣌͠ɺ 2ͷ໨͕ग़Δ, 4ͷ໨͕ग़Δ, 6ͷ໨͕ग़ Δ ྫ2 ͕ൃੜͨ࣌͠ɺ (ද, ཪ), (ཪ, ද) @kataokatsuki 41

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݁Ռͱશࣄ৅ @kataokatsuki 42

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 43

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ى͜Γ͏Δࣄ৅͸ͲΕʁ 1. 1ͷ໨͕ग़ͨ 2. ۮ਺ͷ໨͕ग़ͨ 3. 1Ҏ্3ҎԼͷ໨͕ग़ͨ 4. 7ͷ໨͕ग़ͨ @kataokatsuki 44

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શͯͷ݁Ռ͔ΒͳΔू߹Λʮશࣄ৅ʯ ͱݺͿʢඪຊۭؒ͸ ʣ 1ͷ໨͕ग़ͨࣄ৅ Λߟ͑Δ @kataokatsuki 45

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Q. ͋Δࣄ৅͕ى͜Γ͏Δ͔ʁ A. ͋Δࣄ৅Λߏ੒͢Δ݁Ռશ͕ͯɺ શࣄ৅Λߏ੒͢Δ݁Ռʹؚ·Ε͍ͯΔ͔ʁ ͱଊ͑ͯΈΔ @kataokatsuki 46

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Πϝʔδ x := []int{1} u := []int{1, 2, 3, 4, 5, 6} // canOccur checks if all elements of x can occur in u. func canOccur(x, u []int) bool { for _, xi := range x { found := false for _, ui := range u { if xi == ui { found = true break } } if !found { return false } } return true } @kataokatsuki 47

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— ʢશࣄ৅ʣ — ʢ1ͷ໨͕ग़ͨࣄ৅ʣ Λߏ੒͢Δ݁Ռશ͕ͯ ʹؚ·Ε͍ͯΔɾɾ੒ཱ ͷࣄ৅͸ى͜Γ͏Δ @kataokatsuki 48

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— ʢશࣄ৅ʣ — ʢ7ͷ໨͕ग़ͨࣄ৅ʣ Λߏ੒͢Δ݁Ռશ͕ͯ ʹؚ·Ε͍ͯΔɾɾෆ੒ཱ ͷࣄ৅͸ى͜Γ͏Βͳ͍ @kataokatsuki 49

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1. 1ͷ໨͕ग़ͨ 2. ۮ਺ͷ໨͕ग़ͨ 3. 1Ҏ্3ҎԼͷ໨͕ग़ͨ 4. 7ͷ໨͕ग़ͨ ͋Δࣄ৅Λߏ੒͢Δ݁Ռશ͕ͯɺશࣄ৅Λߏ੒͢Δ݁Ռʹؚ·Ε͍ͯΔ͔ʁ — 1~3͸ ੒ཱ ! ɾɾى͜Γ͏Δ — 4͸ ෆ੒ཱ " ɾɾى͜Γ͏Βͳ͍ @kataokatsuki 50

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֬཰࿦ͱू߹࿦ @kataokatsuki 51

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 52

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ॏཁͳදݱ @kataokatsuki 53

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ࢼߦɾɾ݁ՌΛ֬ఆͤ͞Δʢ1ͭͷ݁ՌΛੜ੒͢Δʣߦҝ ඪຊ఺ ɾɾࢼߦ͔Β֬ఆ͞ΕΔ΋ͷɾ৘ใ ࣄ৅ɾɾඪຊ఺͔ΒͳΔू߹ ඪຊۭؒɾɾશͯͷඪຊ఺͔ΒͳΔू߹ɾࣄ৅ ࠜݩࣄ৅ɾɾ1ͭͷඪຊ఺͔ΒͳΔू߹ɾࣄ৅ @kataokatsuki 54

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ू߹࿦ɾ֬཰࿦ʢ౷ܭֶʣ ֓೦ͷରԠ @kataokatsuki 55

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ू߹࿦ɾ֬཰࿦ʢ౷ܭֶʣͷ֓೦ͷରԠ ू߹࿦ ֬཰࿦ʢ౷ܭֶʣ ݩ ݁Ռɾඪຊ఺ ʢ෦෼ʣू߹ ࣄ৅ શମू߹ શࣄ৅ɾඪຊۭؒ ݩ͕1ͭͷू߹ ࠜݩࣄ৅ @kataokatsuki 56

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ྫ ͍͜͞Ζৼͬͯग़Δ໨ͷ؍࡯ — ࢼߦ ͍͜͞Ζ1ճৼΔ͜ͱ — ඪຊ఺ = 1ͷ໨͕ग़Δ, ... , = 6ͷ໨͕ग़Δ — ඪຊۭؒ = { 1ͷ໨͕ग़Δ, ... , 6ͷ໨͕ग़Δ } = — ࣄ৅ ۮ਺ͷ໨͕ग़ͨ = { 2ͷ໨͕ग़Δ, 4ͷ໨͕ग़Δ, 6ͷ໨͕ग़Δ, ... } = — ࠜݩࣄ৅ 1ͷ໨͕ग़ͨ, 2ͷ໨͕ग़ͨ, ... = @kataokatsuki 57

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ྫ ίΠϯ2ຕΛ౤͛ͨࡍͷ໘ͷ؍࡯ ͦΕͧΕͷίΠϯΛC1, C2ͱ۠ผ — ࢼߦ ίΠϯ2ຕΛ1ճ౤͛Δ͜ͱ — ඪຊ఺ =C1͸දɾC2͸ཪ͕ग़Δ, ... , =C1͸ཪɾC2͸ཪ͕ग़Δ — ඪຊۭؒ { C1͸දɾC2͸ཪ͕ग़Δ, ... , C1͸ཪɾC2͸ཪ͕ग़ͨ } = — ࣄ৅ ද͕1ຕग़ͨ = { C1͸දɾC2͸ཪ͕ग़Δ, C1͸ཪɾC2͸ද͕ग़Δ } = — ࠜݩࣄ৅ C1͸දɾC2͸ཪ͕ग़ͨ, ... = @kataokatsuki 58

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֬཰ͷ֓ཁ @kataokatsuki 59

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 60

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֬཰ͷ෼ྨ ٬؍֬཰ ཧ࿦΍؍࡯౳Ͱ֬཰Λߟ͑Δ 1. ݹయత֬཰ʢཧ࿦తɾ਺ֶతʣ — ৔߹ͷ਺Λߟ͑Δ 2. ౷ܭత֬཰ʢස౓తʣ — Կ౓΋ࢼߦͯ͠ɺͦͷ݁ՌΛ ݩʹ֬཰Λߟ͑Δ 3. ެཧత֬཰ — ެཧΛݩʹ֬཰Λߟ͑Δ ओ؍֬཰ ਓؒͷओ؍ʹج͍ͮͯ֬཰Λߟ͑Δ @kataokatsuki 61

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֬཰ͷ෼ྨ ٬؍֬཰ ཧ࿦΍؍࡯౳Ͱ֬཰Λߟ͑Δ 1. ݹయత֬཰ʢཧ࿦తɾ਺ֶతʣ — ৔߹ͷ਺Λߟ͑Δ 2. ౷ܭత֬཰ʢස౓తʣ — Կ౓΋ࢼߦͯ͠ɺͦͷ݁ՌΛ ݩʹ֬཰Λߟ͑Δ 3. ެཧత֬཰ — ެཧΛݩʹ֬཰Λߟ͑Δ ओ؍֬཰ ਓؒͷओ؍ʹج͍ͮͯ֬཰Λߟ͑Δ @kataokatsuki 62

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ެཧͱ͸ʁ3 ެཧʢ͜͏Γʣ͸ɺ ͦͷଞͷ໋୊Λಋ͖ग़ͨ͢Ίͷલఏͱͯ͠ಋೖ͞ΕΔ ࠷΋جຊతͳԾఆͷ͜ͱͰ͋Δ ٞ࿦ͷग़ൃ఺ʹͳΔ 3 https://ja.wikipedia.org/wiki/%E5%85%AC%E7%90%86 @kataokatsuki 63

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͓·͚ — ެཧɾɾূ໌ൈ͖ͰೝΊΔ΋ͷʢਖ਼͍͠ͱԾఆ͢Δ΋ͷʣ — ໋୊ɾɾެཧ͔Β࿦ཧతʹಋ͔ΕΔ΋ͷ — ఆཧɾɾ໋୊ͷ͏ͪɺಛʹॏཁͳ΋ͷ — ఆٛɾɾ͋Δࣄฑʹ໊લΛ͚ͭΔ͜ͱ @kataokatsuki 64

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ެཧత֬཰ ͋ΔԾఆΛ͓͍ͯ ͦͷԾఆΛຬͨ͢΋ͷ͸֬཰Ͱ͋Δ ͱ͢Δ ৄ͘͠͸֬཰ۭؒ౳Λߟ͑Δඞཁ͕͋Δ @kataokatsuki 65

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͍͜͞ΖΛ1ͭৼΔࢼߦ ग़Δ໨ͷ֬཰͸ͦΕͧΕ͍͘Βʁ @kataokatsuki 66

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ࠜݩࣄ৅ ֬཰ { 1ͷ໨͕ग़Δ } 1/6 { 2ͷ໨͕ग़Δ } 1/6 { 3ͷ໨͕ग़Δ } 1/6 { 4ͷ໨͕ग़Δ } 1/6 { 5ͷ໨͕ग़Δ } 1/6 { 6ͷ໨͕ग़Δ } 1/6 @kataokatsuki 67

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ʮAͷʯ֬཰͸ʮBʯ Aɾɾࣄ৅ Bɾɾ਺஋(0~1) ʮ1ͷ໨͕ग़ͨ֬཰ʯ͸ʮ1/6ʯ @kataokatsuki 68

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֬཰ͱ͸ʁ ͋Δू߹ΛೖྗʹͱΓɺ 0~1ͷ਺஋Λग़ྗ͢Δؔ਺ͱଊ͑Δ ֬཰ = Probability ͱͯ͠ (ू߹) = ਺஋ ͱදݱ͢Δ — ({ 1ͷ໨͕ग़Δ }) = 1/6 — ({ 2ͷ໨͕ग़Δ }) = 1/6 — ({ 2ͷ໨͕ग़Δ, 4ͷ໨͕ ग़Δ, 6ͷ໨͕ग़Δ }) = 1/2 @kataokatsuki 69

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֬཰ม਺ɾ࣮ݱ஋ @kataokatsuki 70

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 71

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͍͜͞ΖΛ1ͭৼΔࢼߦ ʮग़Δ໨ͷظ଴஋ʯ͸ʁ @kataokatsuki 72

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ͷ໨͕ग़Δ֬཰ = ظ଴஋ = = = = @kataokatsuki 73

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͍͜͞ΖΛ1ͭৼΔࢼߦ ग़Δ໨ͷ2ഒͷظ଴஋͸ʁ @kataokatsuki 74

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ظ଴஋ = = = = @kataokatsuki 75

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ࠓ΍ͬͨ͜ͱΛ෼ੳͯ͠ΈΑ͏ʂ @kataokatsuki 76

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͍͜͞ΖΛ1ͭৼΔࢼߦ͔Β͸ʮ6ͭͷࠜݩࣄ৅ʯ͕ߟ͑ΒΕΔ ಘΒΕͨࠜݩࣄ৅1ͭ1ͭʹ ͋Δ਺஋ʢग़ͨ໨orग़ͨ໨ͷ2ഒʣ Λ1ׂͭͣͭΓ౰͍ͯͯΔͱղऍ͢Δ @kataokatsuki 77

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͋Δ਺஋͕ʮग़ͨ໨ͷ1ഒʯ ࠜݩࣄ৅ ͋Δ਺஋ ֬཰ { 1ͷ໨͕ग़Δ } 1 1/6 { 2ͷ໨͕ग़ Δ } 2 1/6 { 3ͷ໨͕ग़ Δ } 3 1/6 { 4ͷ໨͕ग़ Δ } 4 1/6 { 5ͷ໨͕ग़Δ } 5 1/6 { 6ͷ໨͕ग़ Δ } 6 1/6 ͋Δ਺஋͕ʮग़ͨ໨ͷ2ഒʯ ࠜݩࣄ৅ ͋Δ਺஋ ֬཰ { 1ͷ໨͕ग़Δ } 2 1/6 { 2ͷ໨͕ग़ Δ } 4 1/6 { 3ͷ໨͕ग़ Δ } 6 1/6 { 4ͷ໨͕ग़ Δ } 8 1/6 { 5ͷ໨͕ग़Δ } 10 1/6 { 6ͷ໨͕ग़ Δ } 12 1/6 @kataokatsuki 78

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֬཰ม਺ͱ࣮ݱ஋ͱ͸ʁ ࠜݩࣄ৅ʹର͢Δ਺஋ׂΓ౰ͯʹ͓͍ͯ ͋Δू߹ΛೖྗʹͱΓɺ ਺஋Λग़ྗ͢Δؔ਺Λߟ͑Δ ؔ਺Λ֬཰ม਺ ग़ྗ͞ΕΔ਺஋Λ࣮ݱ஋ ͱݴ͏ ֬཰ม਺(ू߹) = ࣮ݱ஋ ྫ ֬཰ม਺Λ ͱ͢Δͱ - 1ͷ໨͕ग़Δ = 1 - 5ͷ໨͕ग़Δ = 5 @kataokatsuki 79

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— ֬཰ม਺ɾɾ — ࣮ݱ஋ɾɾ — ࣄ৅ʢू߹ʣɾɾ ͱ͢Δͱ = ʹ (ू߹)Λೖྗ͢Δͱɺग़ྗ͸ = ࣄ৅ ͕ىͬͨ࣌͜ɺ֬཰ม਺ ͸ ͱͳΔ @kataokatsuki 80

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͋Δ਺஋͕ʮग़ͨ໨ͷ1ഒʯ ࠜݩࣄ৅ ͋Δ਺஋ ֬཰ { 1ͷ໨͕ग़Δ } 1 1/6 { 2ͷ໨͕ग़Δ } 2 1/6 { 3ͷ໨͕ग़Δ } 3 1/6 { 4ͷ໨͕ग़ Δ } 4 1/6 { 5ͷ໨͕ग़Δ } 5 1/6 { 6ͷ໨͕ग़ Δ } 6 1/6 ֬཰ม਺ = 1,2,...,6ʢ6௨Γʣ ͋Δ਺஋͕ʮग़ͨ໨ͷ2ഒʯ ࠜݩࣄ৅ ͋Δ਺஋ ֬཰ { 1ͷ໨͕ग़Δ } 2 1/6 { 2ͷ໨͕ग़Δ } 4 1/6 { 3ͷ໨͕ग़Δ } 6 1/6 { 4ͷ໨͕ग़ Δ } 8 1/6 { 5ͷ໨͕ग़Δ } 10 1/6 { 6ͷ໨͕ग़ Δ } 12 1/6 ֬཰ม਺ = 2,4,...,12ʢ6௨Γʣ @kataokatsuki 81

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֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ܎ @kataokatsuki 82

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 83

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֬཰Λ ֬཰ม਺ɾ࣮ݱ஋Λ࢖ͬͯ දݱͯ͠ΈΑ͏ @kataokatsuki 84

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1ͷ໨͕ग़Δ֬཰Λ Λຬͨ͢ࣄ৅͕ൃੜ͢Δ֬ ཰ ͱݴ͍׵͑ @kataokatsuki 85

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1ͷ໨͕ग़Δࣄ৅ɾू߹ Λຬͨ͢ࣄ৅ɾू߹ @kataokatsuki 86

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7ͷ໨͕ग़Δ֬཰͸ʁ @kataokatsuki 87

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7ͷ໨͕ग़Δࣄ৅ɾू߹ Λຬͨ͢ࣄ৅ɾू߹ @kataokatsuki 88

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ࡉ͔͘ݟͯΈΑ͏ @kataokatsuki 89

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ࣄ৅ 1ͷ໨͕ग़ͨࣄ৅ɾɾ = { 1ͷ໨͕ग़Δ } ͷඪຊ఺Λ ͱදه͢Δͱɺඪຊ఺ ͸2ͭͷ৚݅Λຬͨ͢ 1. ඪຊۭؒͷඪຊ఺Ͱ͋Δʢ݁Ռͱͯ͠ଘࡏ͠͏Δ͔ʹରԠʣ ( Πϯ ) 2. ֬཰ม਺ ͕1ͱͳΔू߹ͷඪຊ఺Ͱ͋Δʢࣄ৅ͷൃੜʹର Ԡʣ ͸1,2Λຬͨ͢ඪຊ఺͔ΒͳΔू߹ @kataokatsuki 90

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ू߹ͷදݱʹ͓͍ͯɺ֎Ԇతه๏Λ࢖͏ͱ ू߹ = { ඪຊ఺ | ඪຊ఺͕ຬͨ͢΂͖৚݅ʢ໋୊ʣ } 1. 2. = { ৚݅1 | ৚݅2 } = ৚݅1͕ʮඪຊ఺ͷେલఏʯ˺ʮඪຊ఺ʯΛද͍ͯ͠Δͱղऍ @kataokatsuki 91

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の目が出る事象・集合 を満たす事象・集合 @kataokatsuki 92

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Կ͕خ͍͠ʁ @kataokatsuki 93

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͋Δࣄ৅͕ൃੜ͢Δ֬཰Λ ʮ֬཰ม਺ ͕͋Δ࣮ݱ஋ͱͳΔ֬཰ʯʹಡΈସ͑Δ͜ͱ͕Ͱ ͖ͨ ޙऀͷํ͕਺ࣜͰධՁ͠΍͍͢ @kataokatsuki 94

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ʮ ͱͳΔू߹ʯΛ୯ʹʮ ʯͱදه͢Δ @kataokatsuki 95

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֬཰ม਺ͷදه͸( )Λলུ͢Δ͜ͱ΋͋Δ @kataokatsuki 96

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·ͱΊΔͱ Λ֬཰ʢີ౓ʣؔ਺ͱݺͿ — ͕཭ࢄܕɾɾ֬཰ؔ਺ — ͕࿈ଓܕɾɾ֬཰ີ౓ؔ਺ @kataokatsuki 97

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ʮ֬཰ʯ͸2௨ΓͷҙຯͰ࢖ΘΕΔ͜ͱ͕ଟ͍ 1. ֬཰ʢີ౓ʣؔ਺ɾɾؔ਺ — ग़Δ໨ͷ֬཰ɾɾ 2. ֬཰ʢີ౓ʣؔ਺ʹಛఆͷू߹Λೖྗͨ͠ग़ྗɾɾ਺஋ — 1ͷ໨͕ग़Δ֬཰ ɾɾ ͲͪΒͷҙຯͰ࢖ΘΕ͍ͯΔ͔ҙࣝͯ͠ղऍ͢Δͱྑ͍ @kataokatsuki 98

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の目が出る事象・集合 を満たす事象・集合 @kataokatsuki 99

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֬཰ม਺ ʹয఺Λ౰ͯͨදݱͱͯ͠ ֬཰ม਺ ͸ʮ֬཰ʢີ౓ʣؔ਺ͷ໊শʯʹै͏ ͱදݱ͞ΕΔ͜ͱ͕͋Δ ʮ ֬཰ʢີ౓ʣؔ਺ͷ໊শʯ ͋Δಛఆͷ֬཰ʢີ౓ʣؔ਺ʹ͸໊લ͕͚ͭΒΕ͓ͯΓ ͦΕΒͷؔ਺͸ʮʙ෼෍ʯͱݺ͹ΕΔ͜ͱ͕ଟ͍ @kataokatsuki 100

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΍΍͍͜͠આ໌͸Ұ౓ऴΘΓʂ — ͓ർΕ༷Ͱͨ͠ @kataokatsuki 101

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֬཰ʢີ౓ʣؔ਺ @kataokatsuki 102

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ 1. ࣄ৅ͱू߹/݁Ռͱݩ 2. ݁Ռͱશࣄ৅ 3. ֬཰࿦ͱू߹࿦ 4. ֬཰ͷ֓ཁ 5. ֬཰ม਺ɾ࣮ݱ஋ 6. ֬཰ɾ֬཰ม਺ɾ࣮ݱ஋ͷؔ ܎ 7. ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 103

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1ͭͷ͍͜͞ΖΛ౤͛Δࢼߦʹ͓͍ͯͷग़Δ໨(=֬཰ม਺ )ͷ֬཰ؔ਺ ·ͱΊͨදه ֬཰ม਺ ͕࣮ݱ஋ ͱͳΔ֬཰ ͕શͯ౳͍࣌͠ ͸Ұ༷෼෍ͱݺ͹ΕΔ @kataokatsuki 104

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͋Δࢼߦɾ֬཰ม਺͸৭ʑߟ͑ΒΕΔ ͕཭ࢄܕ — ίΠϯτεΛෳ਺ճߦ͏ — ද͕ग़ͨճ਺ — ίΠϯτεΛද͕ग़Δ· Ͱߦ͏ — ද͕ग़Δ·Ͱཪ͕ग़ͨ ճ਺ ͕࿈ଓܕ — ೔ຊਓ͔Β1ਓΛબͿ — ͦͷਓͷ਎௕ (cm) — ৽͍͠ిٿΛઃஔͯͭ͠ ͚ͬͺͳ͠ʹ͢Δ — ͦͷిٿͷण໋ (hour) @kataokatsuki 105

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ಛʹॏཁͳ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 106

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཭ࢄܕɾɾೋ߲෼෍ ࿈ଓܕɾɾਖ਼ن෼෍ @kataokatsuki 107

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཭ࢄܕɾɾೋ߲෼෍ @kataokatsuki 108

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— inomial Distribution @kataokatsuki 109

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ίΠϯτεΛ ճߦ͏ࢼߦΛߟ͑Δ - ද͕ग़Δ֬཰Λ - ද͕ग़Δճ਺Λ - ࣮ݱ஋ ผͷදهྫ @kataokatsuki 110

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50ճද͕ग़Δ֬཰ ɾɾ ɾɾ @kataokatsuki 111

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— ҩༀ඼ͷ༗ޮੑςετ — ࢼߦճ਺( ): ਓͷױऀʹ৽ༀΛ౤༩ — ੒ޭ֬཰( ): ҩༀ඼͕ಛఆͷපؾʹରͯ͠༗ޮͰ͋Δ֬཰ — ੒ޭ਺( ): ৽ༀ͕༗ޮͩͬͨױऀͷ਺ — ੡඼ͷ඼࣭؅ཧ — ࢼߦճ਺( ): ݸͷ੡඼ΛϥϯμϜʹநग़͠඼࣭ݕࠪ — ੒ޭ֬཰( ): ੡඼͕ෆྑ඼Ͱ͋Δ֬཰ — ੒ޭ਺( ): ෆྑ඼ͷ਺ — Ξϯέʔτௐࠪ — ࢼߦճ਺( ): ਓʹҙݟௐࠪΛ࣮ࢪ — ੒ޭ֬཰( ): ಛఆͷҙݟ΍ఏҊʹࢍ੒͢Δ֬཰ — ੒ޭ਺( ): ࢍ੒ͨ͠ਓ਺ @kataokatsuki 112

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࿈ଓܕɾɾਖ਼ن෼෍ @kataokatsuki 113

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— ormal Distribution @kataokatsuki 114

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਎௕͕171~172cmͰ͋Δ֬཰ ঁੑɾɾ உੑɾɾ h!ps://www.e-stat.go.jp/dbview?sid=0003224177 @kataokatsuki 115

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֬཰ͱ֬཰ʢີ౓ʣؔ਺ @kataokatsuki 116

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ʮ֬཰ʢີ౓ʣؔ਺ͷ໘ੵ=֬཰ʯͷΠϝʔδ @kataokatsuki 117

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ਪଌ౷ܭֶ @kataokatsuki 118

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ΞδΣϯμ 1. ౷ܭֶͷ֓ཁ 2. هड़౷ܭֶ 3. ू߹࿦ 4. ֬཰࿦ 5. ਪଌ౷ܭֶ @kataokatsuki 119

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ਪଌ౷ܭֶͷ എޙʹ͋Δ࢓૊Έͱ͸ʁ @kataokatsuki 120

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@kataokatsuki 121

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࢓૊Έ ≒ ฼ूஂͷʮ֬཰ʢີ౓ʣؔ਺ɾ֬཰෼෍ʯ ෼෍Λ֬ఆͤ͞Δύϥϝʔλ͕ʮ฼਺ʯ — ฼ूஂ = ෼ੳର৅શମ — ฼਺ != ෼฼(≒฼ूஂͷαΠζ) , ) @kataokatsuki 122

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ਖ਼ن෼෍ - ฼ฏۉ - ฼෼ࢄ ͕෼෍ΛఆΊΔ ௚ઢ - ܏͖ - ੾ย ͱ ͕௚ઢ͕ఆΊΔ @kataokatsuki 123

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฼ฏۉ͕มΘΔͱʁ ෼෍͸ࠨӈʹฏߦҠಈ — ͹Β͖ͭ͸มΘΒͳ͍ — ෼෍ͷܗ͸ಉ͡ @kataokatsuki 124

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฼෼ࢄ͕มΘΔͱʁ ෼෍ͷܗঢ়͕มԽ — ฏۉ͸มΘΒͳ͍ — ෼ࢄ͕খ͍͞΄Ͳʮઑͬ ͨʯܗ — ฏۉ͔Β཭Εͨ஋͕ग़ ʹ͍͘ @kataokatsuki 125

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ਪଌ౷ܭֶͰ͸฼਺ʹಛʹ஫໨͢Δ͜ͱ͕ଟ͍ ෼෍ͷछྨ͸ - ܦݧతʹʮਖ਼ن෼෍ʯͳͲಛఆͷ෼෍ͰԾఆ - ʮະ஌Ͱ͋Δʯͱͯ͠ਪఆ͢Δʢະ஌Ͱ͋Δͱͨ͠ํ͕ޡࠩ ͕େ͖͍ʣ ͱѻ͏৔߹͕ଟ͍ @kataokatsuki 126

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఺ਪఆɾ۠ؒਪఆɾݕఆ ؆୯ͳ঺հ @kataokatsuki 127

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఺ਪఆ ฼਺ΛϐϯϙΠϯτͰਪఆ͢Δ — ྫ: — ͋Δௐࠪσʔλʢඪຊʣ͔ΒಘΒΕͨฏۉʢඪຊฏۉʣ͕172cmͩͱܭࢉ͞Εͨ — ͳͷͰɺ೔ຊਓͷ੒ਓஉੑͷฏۉ਎௕͸172cmͰ͋Δ — ϝϞ: — ඪຊฏۉࣗମ΋֬཰ม਺Ͱ͋Γɺ͹Β͖ͭΛ࣋ͭ — ඪຊʹؚ·ΕΔਓؒશһͷ਎௕͕200cmͰɺඪຊฏۉ͕200cmʹͳΔՄೳੑ΋ 0Ͱ͸ͳ͍ @kataokatsuki 128

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۠ؒਪఆ ฼਺͕͋Δ֬཰Ҏ্Ͱؚ·ΕΔͱߟ͑ΒΕΔൣғΛਪఆ — ྫ: — ࠓճͷඪຊ͔Βɺ೔ຊਓஉੑͷ95%৴པ͕۠ؒ[171.2cm, 173.8cm]ͱܭࢉ͞Εͨ — ͭ·Γɺ͜ͷ͕۠ؒ೔ຊਓஉੑͷฏۉ਎௕ΛؚΉ֬཰͸95%Ͱ͋Δͱਪఆ͞Ε Δ — ϝϞ: — ৴པ۠ؒ: ͦͷൣғ͕฼ฏۉΛؚΉ֬཰(৴པ౓)Λ%Ͱද͢ — ྫ: 95%৴པ۠ؒ = ͦͷൣғ͕฼ฏۉΛؚΉ֬཰͸95% @kataokatsuki 129

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ݕఆ ͋ΔԾઆ͕ࢧ࣋͞ΕΔ͔Λ൑அ͢Δ — ྫ:ʮ೔ຊਓஉੑͷฏۉ਎௕͸165cmະຬʯͱ͍͏ԾઆΛஔ͘ — ඪຊฏۉ͕172cmͩͬͨͱ͢Δ — Ծઆ͕ਖ਼͍͠ͱ͢Δ࣌ɺඪຊฏۉ͕172cmҎ্ͱͳΔ֬཰Λܭࢉ͢Δ — ͦͷ֬཰͕͋ΔܾΊͨᮢ஋ΑΓ΋খ͍͞ɾɾԾઆ͕ؒҧ͍ͬͯΔͱ൑அ — ϝϞ: — ᮢ஋ɾɾ༗ҙਫ४ͱ͍͍ɺԾઆΛؒҧ͍ͱ൑அʢغ٫ͱ͍͏ʣ͢Δ͔Ͳ͏͔ͷج४ͱ ͳΔ֬཰ͷ஋ — Ұൠతʹ͸ɺ5%΍1%ʹઃఆ͢Δ͜ͱ͕ଟ͍ @kataokatsuki 130

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ࠓ·Ͱͷ෮श @kataokatsuki 131

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౷ܭֶʹ͸2छྨ͋Δ هड़౷ܭֶ (ಘΒΕͨσʔλࣗମΛߟ࡯͢Δɾڵຯ͕͋Δ) ਪଌ౷ܭֶ (ಘΒΕͨσʔλͷഎޙʹ͋Δ΋ͷΛߟ࡯͢Δɾڵຯ͕͋Δ) ౷ܭֶͰ͸ू߹࿦ɾ֬཰࿦Λར༻͢Δ - ͬ͘͟ΓͷΠϝʔδΛ͓࣋ͬͯ͘ͱ͋ͱͷษڧ͕͠΍͍͢ ਪଌ౷ܭֶ͸େ͖͘3ͭʹ෼͚ΒΕΔ - ఺ਪఆ - ۠ؒਪఆ - ݕఆ @kataokatsuki 132

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ࠓճਪଌ౷ܭֶͰѻͬͨߟ͑ํ͸ ʮස౓ओٛʯ ʹଐ͢Δ΋ͷ @kataokatsuki 133

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ਪଌ౷ܭֶͷ೿ൊ — ස౓ओٛ — ֬཰͸ʮࢼߦΛ܁Γฦͨ࣌͠ͷස౓ʯ — ϕΠζओٛ — ֬཰͸ʮ৴೦ͷ౓߹͍ʯ @kataokatsuki 134

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͜ΕΒ͸·͍͔ͨͭ — ࠓ೔͸͜͜·Ͱ @kataokatsuki 135

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ऴΘΓ — ͋Γ͕ͱ͏͍͟͝·ͨ͠ @kataokatsuki 136

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ࢀߟจݙ — ౷ܭֶೖ໳ ౦ژେֶڭཆֶ෦౷ܭֶڭࣨฤ — ݱ୅਺ཧ౷ܭֶͷجૅ ٱอ઒ୡ — σʔλղੳͷͨΊͷ౷ܭϞσϦϯάೖ໳ ٱอ୓໻ — σʔλղੳͷͨΊͷ਺ཧ౷ܭೖ໳ ٱอ઒ୡ໵ — ස౓ओٛ౷ܭֶΛʮ׬શʹཧղʯ͠Α͏ https://speakerdeck.com/ ueniki/pin-du-zhu-yi-tong-ji-xue-wo-wan-quan-nili-jie-siyou) ͦͷଞͨ͘͞Μͷૉ੖Β͍͠ڭࡐ @kataokatsuki 137