ᱣᱮᱨᱤᱭᱮᱱᱥ
ᱪᱮᱫᱟᱜ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱩᱬ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ; ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱟᱨᱵᱟᱝ ᱚᱠᱛᱚ ᱨᱮ ᱟᱣᱥᱚᱛ ᱛᱮ ᱦᱟᱨᱟᱣᱚᱜ ᱴᱟᱠᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱟᱶ ᱢᱤᱫ ᱥᱴᱨᱮᱴ ᱚᱯ ᱟᱨ ᱢᱤᱫ ᱟᱨᱟᱜ ᱵᱟᱡᱤ ᱵᱷᱮᱜᱟᱨ ᱠᱷᱮᱞ ᱞᱮᱠᱟ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ᱾
ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱷᱮᱨᱟᱣ ᱨᱮᱡᱟᱞᱴ ᱪᱮᱫ ᱦᱟᱹᱵᱤᱡ ᱯᱟᱥᱱᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱢᱟᱯ ᱮᱫᱟ᱾ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱭᱩᱱᱤᱴ ᱨᱮ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ ᱵᱮᱥᱤ 34 ᱟᱨ ᱟᱨᱟᱜ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ ᱵᱮᱥᱤ 1 ᱠᱟᱱᱟ᱾
ᱢᱤᱫ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱡᱟᱦᱟᱸ ᱵᱟᱡᱤ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → p ᱥᱟᱶ W ᱨᱮ 1 ᱮᱢᱚᱜ-ᱟ, ᱚᱱᱟ ᱨᱮ ᱡᱚᱛᱚ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱨᱮᱡᱟᱞᱴ ᱫᱚ p ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱥᱟᱶ +W ᱟᱨ 1 − p ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱥᱟᱶ −1 ᱠᱟᱱᱟ᱾ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱵᱟᱡᱤ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ pW − (1 − p) = −1/37 ᱠᱟᱱᱟ᱾ ᱣᱮᱨᱤᱭᱮᱱᱥᱜᱚᱱᱤᱛᱣᱮᱨᱤᱭᱮᱱᱥᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱷᱮᱨᱟᱣ ᱨᱮᱡᱟᱞᱴ ᱛᱤᱱᱟᱹᱜ ᱯᱟᱥᱱᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱯᱲᱟᱣ᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱵᱟᱹᱲᱛᱤ, ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ E[X²] − EV² = pW² + (1 − p) − (1/37)² ᱠᱟᱱᱟ᱾ ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08᱾ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ: 18/37 + 19/37 − 0.0007 ≈ 0.999᱾
ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱞᱟᱹᱜᱤᱫ ᱱᱚᱣᱟ ᱨᱮᱭᱟᱜ ᱢᱟᱱᱮ
ᱟᱡᱟᱫ ᱜᱷᱩᱨᱟᱹᱣᱜᱚᱱᱤᱛᱟᱡᱟᱫ ᱜᱷᱩᱨᱟᱹᱣᱢᱟᱨᱮ ᱪᱮᱫ ᱦᱚᱸ ᱦᱩᱭ ᱠᱷᱟᱱ ᱦᱚᱸ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱢᱤᱫ ᱞᱮᱠᱟ ᱜᱮ᱾ ᱱᱚᱶᱟ ᱥᱟᱭᱤᱴ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱦᱤᱥᱟᱹᱵ ᱨᱮᱭᱟᱜ ᱵᱮᱥ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱠᱚ ᱡᱚᱲᱟᱣᱚᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱢᱤᱫ ᱛᱷᱤᱨ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱥᱟᱶ N ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱚᱛᱚ ᱨᱮᱭᱟᱜ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱚ N × ᱵᱟᱡᱤ ᱴᱟᱠᱟ² × σ² ᱠᱟᱱᱟ, ᱟᱨ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱜᱚᱱᱤᱛᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱣᱮᱨᱤᱭᱮᱱᱥ ᱨᱮᱭᱟᱜ ᱵᱚᱜᱚ ᱢᱩᱞ; ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱠᱷᱚᱱ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱥᱟᱦᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ σ × ᱵᱟᱡᱤ ᱴᱟᱠᱟ × √N ᱠᱟᱱᱟ᱾ $10 ᱥᱟᱶ 100 ᱜᱷᱩᱨᱟᱹᱣ: ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ $584 ᱟᱨ ᱟᱨᱟᱜ ᱞᱟᱹᱜᱤᱫ $100 ᱠᱟᱱᱟ, ᱵᱟᱨᱭᱟ ᱜᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱟᱸᱫᱟᱡᱽ −$27 ᱜᱷᱮᱨᱟᱣ᱾ ᱢᱤᱫ ᱠᱷᱮᱞᱚᱸᱰ ᱫᱚ ᱥᱟᱭ ᱥᱟᱭ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱫᱩᱞᱩᱵ ᱮ ᱧᱮᱞᱟ; ᱮᱴᱟᱜ ᱫᱚ ᱞᱟᱦᱟᱭ ᱞᱟᱦᱟᱭ ᱥᱟᱨᱮᱡ ᱮ ᱧᱮᱞᱟ᱾ ᱵᱟᱨᱭᱟ ᱜᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱫᱟᱢ ᱠᱤᱱ ᱮᱢ ᱮᱫᱟ᱾
ᱣᱮᱨᱤᱭᱮᱱᱥ ᱟᱨ ᱥᱤᱥᱴᱮᱢ
ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱᱥᱴᱨᱮᱴᱮᱡᱤᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱᱢᱟᱨᱮ ᱨᱮᱡᱟᱞᱴ ᱞᱮᱠᱟ ᱛᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱚᱫᱚᱞ ᱡᱟᱦᱟᱸᱱ ᱱᱤᱭᱚᱢ᱾ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱲᱦᱟᱣᱟ, ᱯᱚᱡᱤᱴᱤᱵᱷ ᱡᱤᱛ ᱛᱟᱭᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱭᱩᱱᱤᱴ ᱨᱮ EV ᱵᱟᱝ ᱵᱚᱫᱚᱞ ᱮᱫᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱟᱨ ᱵᱟᱸᱴᱟᱣ ᱨᱮᱭᱟᱜ ᱫᱷᱟᱸᱪᱟ ᱵᱟᱨᱭᱟ ᱜᱮ ᱵᱚᱫᱚᱞ ᱮᱫᱟ᱾ ᱢᱟᱨᱴᱤᱝᱜᱮᱞᱥᱴᱨᱮᱴᱮᱡᱤᱢᱟᱨᱴᱤᱝᱜᱮᱞᱡᱚᱛᱚ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ᱾ ᱱᱚᱶᱟ ᱪᱮᱫ ᱮ ᱠᱟᱹᱢᱤᱭᱟ ᱟᱨ ᱪᱮᱫ ᱵᱟᱭ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱦᱟᱹᱴᱤᱧ ᱨᱮ ᱧᱮᱞ ᱯᱮ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱟᱹᱰᱤ ᱟᱹᱰᱤ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱠᱚᱢ ᱮᱫᱟ (ᱟᱭᱢᱟ ᱦᱩᱰᱤᱧ ᱡᱤᱛ) ᱟᱨ ᱢᱤᱫ ᱢᱚᱴᱟ ᱪᱩᱞᱟᱹ ᱡᱚᱲᱟᱣ ᱮᱫᱟ (ᱜᱟᱱ ᱜᱟᱱ ᱦᱩᱭᱩᱜ ᱢᱟᱨᱟᱝ ᱦᱟᱹᱱᱤ); ᱚᱱᱟ ᱪᱩᱞᱟᱹ ᱞᱟᱹᱜᱤᱫ ᱡᱚᱛᱚ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱚ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤᱥᱴᱨᱮᱴᱮᱡᱤᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱡᱚᱛᱚ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱱᱚᱶᱟ ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱯᱟᱨᱚᱞᱤᱥᱴᱨᱮᱴᱮᱡᱤᱯᱟᱨᱚᱞᱤᱯᱚᱡᱤᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ: ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱰᱚᱵᱚᱞ, ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱟᱨᱵᱟᱝ ᱞᱟᱜᱟᱛᱟᱨ ᱯᱮ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱫᱚᱦᱲᱟ ᱮᱛᱚᱦᱚᱵ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱩᱞᱴᱟᱹ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱩᱞᱴᱟᱹ ᱠᱟᱹᱢᱤ ᱮᱫᱟ᱾ ᱥᱤᱥᱴᱮᱢ ᱵᱟᱪᱷᱟᱣ ᱫᱚ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱷᱟᱸᱪᱟ ᱵᱟᱪᱷᱟᱣ ᱠᱟᱱᱟ; ᱟᱣᱥᱚᱛ ᱫᱚ ᱵᱟᱪᱷᱟᱣ ᱞᱟᱹᱜᱤᱫ ᱵᱟᱹᱱᱩᱜ-ᱟ᱾
- p10 −$500
- p25 −$500
- ᱢᱤᱰᱤᱭᱟᱱ −$500
- p75 +$40
- p90 +$1,120
ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤᱯᱟᱨᱚᱞᱤ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤ (ᱩᱞᱴᱟᱹ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ)
ᱠᱷᱮᱞᱚᱸᱰ ᱞᱟᱹᱜᱤᱫ ᱪᱮᱫᱟᱜ ᱱᱚᱣᱟ ᱞᱟᱹᱠᱛᱤ ᱜᱮᱭᱟ
ᱣᱮᱨᱤᱭᱮᱱᱥ ᱛᱮ ᱜᱮ ᱦᱩᱰᱤᱧ ᱥᱮᱥᱚᱱ ᱫᱚ ᱵᱟᱝ ᱵᱩᱡᱷᱟᱹᱣ ᱫᱟᱲᱮᱭᱟᱜ ᱟᱨ ᱡᱮᱞᱮᱧ ᱥᱮᱥᱚᱱ ᱫᱚ ᱵᱩᱡᱷᱟᱹᱣ ᱫᱟᱲᱮᱭᱟᱜ ᱦᱩᱭᱩᱜ-ᱟ᱾ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ σ = $100 ᱟᱨ EV = −$27 ᱥᱟᱶ, ᱵᱟᱲᱛᱤ ᱫᱚ ᱦᱩᱞᱟᱹᱢ ᱨᱮᱭᱟᱜ ᱯᱩᱱ ᱦᱟᱹᱴᱤᱧ ᱠᱷᱚᱱ ᱢᱤᱫ ᱠᱟᱱᱟ ᱟᱨ ᱡᱤᱛ ᱥᱮᱥᱚᱱ ᱫᱚ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱠᱟᱛᱷᱟ ᱠᱟᱱᱟ᱾ 10,000 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ EV ᱫᱚ −$2,700 ᱟᱨ σ ᱫᱚ $1,000 ᱠᱟᱱᱟ; ᱱᱤᱛ ᱵᱟᱲᱛᱤ ᱫᱚ ᱦᱩᱞᱟᱹᱢ ᱠᱷᱚᱱ ᱡᱷᱚᱛᱚ ᱯᱮ ᱜᱩᱱ ᱠᱟᱱᱟ ᱟᱨ ᱡᱤᱛ ᱫᱚ ᱯᱮ-ᱥᱤᱜᱽᱢᱟ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱠᱟᱱᱟ᱾ ᱦᱩᱰᱤᱧ ᱚᱠᱛᱚ ᱨᱮ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱚ ᱠᱷᱮᱞᱚᱸᱰ ᱨᱮᱭᱟᱜ ᱜᱟᱛᱮ, ᱟᱨ ᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱨᱮᱭᱟᱜ᱾
ᱢᱤᱫᱚᱞ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱣᱮᱨᱤᱭᱮᱱᱥ
ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱭᱢᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱠᱚ ᱥᱟᱹᱜᱟᱹᱭ ᱢᱮᱱᱟᱜ-ᱟ (17 ᱩᱫᱩᱜᱚᱜ ᱠᱷᱟᱱ ᱦᱮᱸᱫᱮᱵᱟᱡᱤᱦᱮᱸᱫᱮ18 ᱦᱮᱸᱫᱮ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱱᱣᱟᱨ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱟᱨ ᱫᱚᱥᱟᱨ ᱰᱚᱡᱮᱱᱵᱟᱡᱤᱰᱚᱡᱮᱱ1–12, 13–24 ᱟᱨᱵᱟᱝ 25–36, ᱵᱷᱩᱜᱛᱟᱱ 2:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱦᱚᱸ ᱡᱤᱛᱚᱜ-ᱟ), ᱚᱱᱟᱛᱮ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱠᱚ ᱥᱚᱡᱮ ᱵᱟᱝ ᱡᱚᱲᱟᱣᱚᱜ-ᱟ᱾ ᱵᱟᱡᱤ ᱵᱮᱱᱟᱣᱤᱡ ᱦᱟᱹᱛᱤᱭᱟᱹᱨ ᱫᱚ ᱡᱚᱛᱚ 37 ᱨᱮᱡᱟᱞᱴ ᱞᱮᱠᱷᱟ ᱠᱟᱛᱮ ᱡᱟᱦᱟᱸᱱ ᱪᱤᱯᱴᱟᱠᱟᱪᱤᱯᱛᱷᱤᱠ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱪᱤᱱᱦᱟᱹ ᱴᱚᱠᱮᱱ, ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱞᱮᱭᱟᱣᱴ ᱨᱮ ᱫᱚᱦᱚᱜ-ᱟ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱪᱮᱠ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ ᱴᱷᱤᱠ ᱵᱟᱸᱴᱟᱣ ᱦᱤᱥᱟᱹᱵ ᱮᱫᱟ, ᱟᱨ ᱱᱚᱣᱟ ᱜᱮ ᱫᱚ ᱢᱤᱫ ᱜᱚᱴᱟᱝ ᱴᱷᱤᱠ ᱦᱚᱨ ᱠᱟᱱᱟ᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱵᱟᱝ᱾ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱢᱮᱱᱟᱜ-ᱟ᱾ ᱵᱮᱥᱤ ᱣᱮᱨᱤᱭᱮᱱᱥ ᱢᱮᱱᱮᱛᱮ ᱚᱱᱟ ᱜᱷᱮᱨᱟᱣ ᱟᱹᱰᱤ ᱚᱥᱟᱨ ᱫᱩᱞᱩᱵ᱾
ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤᱵᱟᱡᱤᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤᱟᱨᱟᱜ/ᱦᱮᱸᱫᱮ, ᱵᱤᱡᱳᱲ/ᱡᱳᱲ, ᱢᱟᱨᱟᱝ/ᱦᱩᱰᱤᱧ᱾ 18 ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 1:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →, ᱡᱚᱛᱚ ᱭᱩᱱᱤᱴ ᱨᱮ σ ≈ 1᱾ ᱞᱟ ᱯᱟᱨᱛᱟᱡᱽᱱᱤᱭᱚᱢᱞᱟ ᱯᱟᱨᱛᱟᱡᱽᱯᱷᱨᱮᱧᱪ ᱱᱤᱭᱚᱢ: ᱡᱤᱨᱚ ᱦᱤᱡᱩᱜ ᱞᱮᱠᱷᱟᱱ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱫᱷᱟ ᱨᱩᱣᱟᱹᱲᱚᱜ-ᱟ᱾ ᱚᱱᱟ ᱵᱟᱡᱤ ᱠᱚ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱟᱫᱷᱟ, 1.35% ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱟᱶ ᱟᱨᱦᱚᱸ ᱠᱚᱢ, ᱟᱨ ᱚᱱᱟ ᱫᱚ ᱟᱣᱥᱚᱛ ᱦᱚᱸ ᱵᱮᱥ ᱮᱫᱟ᱾
ᱡᱚᱛᱚ ᱰᱚᱞᱟᱨ ᱨᱮ ᱟᱸᱫᱟᱡᱽ ᱞᱟᱵᱷ ᱫᱚ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱜᱮ; ᱣᱮᱨᱤᱭᱮᱱᱥ ᱫᱚ ᱥᱩᱢᱩᱝ ᱠᱮᱥᱤᱱᱳ ᱨᱮᱭᱟᱜ ᱟᱹᱢᱫᱟᱹᱱᱤ ᱪᱮᱫ ᱞᱮᱠᱟ ᱩᱪᱟᱹ ᱞᱟᱛᱟᱨ ᱦᱩᱭᱩᱜ-ᱟ ᱚᱱᱟ ᱵᱚᱫᱚᱞ ᱮᱫᱟ, ᱟᱨ ᱠᱮᱥᱤᱱᱳ ᱨᱮ ᱚᱱᱟ ᱥᱚᱢᱟᱱ ᱞᱟᱹᱜᱤᱫ ᱦᱟᱡᱟᱨ ᱦᱟᱡᱟᱨ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱢᱮᱱᱟᱜ ᱠᱚᱣᱟ᱾
ᱜᱚᱱᱤᱛ ᱥᱟᱶ ᱨᱟᱹᱥᱠᱟᱹ
ᱱᱚᱶᱟ ᱠᱚ ᱯᱩᱭᱞᱩ ᱟᱯᱮ ᱛᱮ ᱠᱩᱨᱩᱢᱩᱴᱩ ᱯᱮ᱾ ᱢᱤᱫ ᱢᱤᱫ ᱥᱚᱢᱟᱫᱷᱟᱱ ᱫᱚ ᱩᱠᱩ ᱢᱮᱱᱟᱜ-ᱟ; ᱛᱮᱭᱟᱨ ᱦᱩᱭ ᱠᱟᱛᱮ ᱡᱷᱤᱡᱽ ᱯᱮ᱾
ᱵᱟᱨ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱤᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱪᱟᱠᱟ ᱨᱮ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱦᱟᱹᱵᱤᱡ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ $1 ᱵᱟᱡᱤ ᱠᱤᱱ ᱞᱟᱜᱟᱣᱟ, ᱢᱤᱫᱴᱮᱱ ᱡᱚᱛᱚ ᱚᱠᱛᱚ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ, ᱮᱴᱟᱜᱟᱜ ᱡᱚᱛᱚ ᱚᱠᱛᱚ 17 ᱨᱮ᱾ ᱢᱩᱪᱟᱹᱫ ᱨᱮ ᱚᱠᱟᱭ ᱞᱟᱵᱷ ᱨᱮ ᱛᱟᱦᱮᱸ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱵᱮᱥᱤ?
ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ
ᱛᱮᱞᱟ 17 ᱨᱮ ᱠᱷᱮᱞᱚᱸᱰ: 50.9%, ᱟᱨᱟᱜ ᱨᱮᱭᱟᱜ 35.5% ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣ ᱠᱟᱛᱮ᱾ ᱵᱟᱨᱭᱟ ᱜᱮ ᱟᱣᱥᱚᱛ ᱛᱮ $2.70 ᱠᱤᱱ ᱦᱟᱨᱟᱣᱟ᱾
ᱟᱨᱟᱜ: 100 ᱠᱷᱚᱱ 51 ᱥᱮ ᱵᱮᱥᱤ ᱡᱤᱛ ᱦᱩᱭ ᱠᱷᱟᱱ ᱠᱷᱮᱞᱚᱸᱰ ᱞᱟᱵᱷ ᱨᱮ ᱛᱟᱦᱮᱸᱭᱟ, ᱡᱚᱛᱚ ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → 18/37᱾ ᱵᱟᱭᱱᱚᱢᱤᱭᱟᱞ ᱵᱟᱸᱴᱟᱣ 35.5% ᱮ ᱮᱢᱟ, ᱟᱨ ᱴᱷᱤᱠ 50 ᱡᱤᱛ, ᱵᱟᱨᱟᱵᱟᱨ, ᱟᱨᱦᱚᱸ 7.7%᱾
ᱮᱞ 17: ᱡᱚᱛᱚ ᱡᱤᱛ $36 ᱨᱩᱣᱟᱹᱲ ᱮᱢᱟ, ᱚᱱᱟᱛᱮ ᱵᱟᱨ ᱡᱤᱛ (−$28) ᱫᱚ ᱵᱟᱝ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ ᱟᱨ ᱯᱮ (+$8) ᱥᱮᱴᱮᱨᱚᱜ-ᱟ᱾ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 1/37 ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱮ ᱯᱮ ᱥᱮ ᱵᱮᱥᱤ ᱦᱤᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ 50.9%᱾
ᱥᱴᱨᱮᱴ ᱚᱯ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱥᱤ ᱫᱷᱟᱣ ᱞᱟᱵᱷ ᱨᱮ ᱛᱟᱦᱮᱸᱭᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱚᱱᱟᱜ ᱨᱮᱡᱟᱞᱴ ᱫᱚ ᱵᱮᱥᱤ ᱩᱪᱟᱹᱲ ᱞᱟᱛᱟᱨ: ᱢᱤᱫ ᱦᱤᱴ ᱠᱚᱢ ᱥᱮ ᱵᱮᱥᱤ ᱨᱮᱡᱟᱞᱴ ᱫᱚ $36 ᱮ ᱥᱟᱨᱮᱡᱟ, ᱟᱨ ᱦᱟᱹᱱᱤ ᱨᱮ ᱢᱮᱱᱟᱜ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱫᱚ ᱟᱭᱢᱟ ᱫᱷᱟᱣ ᱵᱮᱥᱤ ᱦᱟᱹᱱᱤ ᱨᱮ ᱛᱟᱦᱮᱸᱱᱟ᱾ ᱵᱚᱞᱢᱟᱱ (Bollman, 2024) ᱟᱢᱮᱨᱤᱠᱟᱱ ᱮᱞ ᱠᱚ ᱮ ᱮᱢ ᱟᱠᱟᱫᱟ, 26.5% ᱟᱨ 49.2%᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ᱾ ᱢᱤᱫᱴᱟᱹᱝ ᱫᱚ ᱚᱱᱟ ᱵᱟᱵᱚᱛ ᱨᱟᱜ ᱨᱟᱜ ᱛᱮ ᱞᱟᱹᱭᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.