ᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱥᱮᱴᱮᱨ: ᱨᱩᱞᱮᱴ ᱨᱮ ᱢᱟᱨᱟᱝ ᱮᱞ ᱨᱮᱭᱟᱜ ᱱᱤᱭᱚᱢ
ᱟᱣᱥᱚᱛ ᱫᱚ ᱪᱮᱫ ᱞᱮᱠᱟ −2.70% ᱥᱮᱫ ᱛᱷᱤᱨᱚᱜ-ᱟ, ᱟᱨ ᱚᱱᱟ ᱫᱚ ᱪᱮᱫᱟᱜ ᱢᱚᱱ ᱨᱮᱭᱟᱜ ᱵᱷᱟᱵᱱᱟ ᱠᱷᱚᱱ ᱵᱟᱹᱲᱛᱤ ᱚᱠᱛᱚ ᱦᱟᱛᱟᱣ-ᱟ᱾
ᱜᱷᱩᱨᱟᱹᱣ ᱡᱟᱦᱟᱸ ᱞᱮᱠᱟ ᱡᱚᱢᱟ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ, ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱦᱟᱹᱱᱤ ᱫᱚ −1/37 ᱥᱮᱫ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ, ᱟᱨ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱯᱟᱥᱱᱟᱣ ᱫᱚ 1/√N ᱞᱮᱠᱟ ᱦᱩᱰᱤᱧᱚᱜ-ᱟ᱾ ᱟᱨᱟᱜ ᱨᱮ 1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱟᱣᱥᱚᱛ ᱫᱚ ᱡᱟᱹᱥᱛᱤ ᱛᱮ ᱟᱸᱫᱟᱡᱽ ᱠᱷᱚᱱ ±3% ᱵᱷᱤᱛᱤᱨ ᱛᱟᱦᱮᱸᱱᱟ᱾
ᱢᱟᱨᱟᱝ ᱮᱞ ᱨᱮᱭᱟᱜ ᱱᱤᱭᱚᱢ
ᱟᱡᱟᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱪᱟᱹᱞᱩ ᱟᱣᱥᱚᱛ ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝᱡᱮᱞᱮᱧ ᱚᱠᱛᱚ ᱨᱮ ᱢᱤᱫ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ᱾ ᱡᱚᱛᱚ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱵᱟᱡᱤ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −1/37᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱮᱫ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ᱾ ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱛᱮ N ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ, ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱫᱚ −1/37 ᱟᱨ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱜᱚᱱᱤᱛᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱣᱮᱨᱤᱭᱮᱱᱥ ᱨᱮᱭᱟᱜ ᱵᱚᱜᱚ ᱢᱩᱞ; ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱠᱷᱚᱱ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱥᱟᱦᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → 1/√N᱾ N = 100 ᱨᱮ ᱱᱚᱶᱟ ᱯᱟᱥᱱᱟᱣ ᱫᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ 10%, ᱡᱟᱦᱟᱸ ᱫᱚ 2.7% ᱥᱚᱝᱠᱮᱛ ᱠᱷᱚᱱ ᱠᱚᱢ ᱵᱮᱥᱤ ᱯᱩᱱ ᱫᱷᱟᱣ᱾ N = 1,000 ᱨᱮ ᱱᱚᱶᱟ 3.2%, ᱥᱚᱝᱠᱮᱛ ᱞᱮᱠᱟ ᱜᱮ᱾ N = 10,000 ᱨᱮ ᱱᱚᱶᱟ 1%, ᱟᱨ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱫᱚ ᱯᱩᱨᱟᱹ ᱧᱮᱞᱚᱜ-ᱟ᱾ ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱫᱚ ᱵᱟᱝ ᱧᱮᱞᱚᱜ-ᱟ, ᱢᱤᱫ ᱥᱮᱨᱢᱟ ᱨᱮ ᱫᱚ ᱵᱷᱩᱞ ᱵᱟᱹᱱᱩᱜ-ᱟ᱾
ᱪᱮᱫ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ ᱟᱨ ᱪᱮᱫ ᱵᱟᱝ
ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱫᱚ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ᱾ ᱡᱚᱛᱚ ᱫᱚ ᱵᱟᱝ: N ᱡᱟᱦᱟᱸ ᱞᱮᱠᱟ ᱵᱟᱹᱲᱛᱤᱭᱚᱜ-ᱟ, ᱚᱱᱟ ᱞᱮᱠᱟ ᱜᱮ ᱡᱚᱛᱚ ᱫᱚ ᱡᱤᱨᱚ ᱠᱷᱚᱱ ᱟᱨᱦᱚᱸ ᱥᱟᱹᱝᱜᱤᱧ ᱪᱟᱞᱟᱜ-ᱟ, ᱟᱸᱫᱟᱡᱽ ᱛᱮ N ᱨᱮᱭᱟᱜ ᱠᱚᱢ ᱵᱮᱥᱤ 2.7%, ᱟᱨ ᱚᱱᱟ ᱪᱟᱨᱤᱫᱤᱥᱟᱹ √N ᱯᱟᱥᱱᱟᱣ ᱥᱟᱶ᱾ $10 ᱛᱮ 10,000 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱮᱞ ᱠᱟᱫ ᱠᱷᱮᱞᱚᱸᱰ ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱛᱮ $2,700 ᱦᱟᱨᱟᱣ ᱨᱮ ᱛᱟᱦᱮᱸᱱᱟᱭ, $1,000 ᱠᱚᱢ ᱵᱮᱥᱤ᱾ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱪᱟᱹᱞᱩ ᱦᱟᱹᱴᱤᱧ ᱫᱚ ᱢᱟᱦᱟᱸ ᱞᱟᱦᱟ ᱠᱷᱚᱱ 48.65% ᱥᱮᱫ ᱛᱷᱤᱨ ᱮᱱᱟ; ᱪᱟᱹᱞᱩ ᱵᱮᱞᱮᱱᱥ ᱫᱚ ᱚᱠᱟ ᱨᱮ ᱦᱚᱸ ᱵᱟᱝ ᱛᱷᱤᱨ ᱟᱠᱟᱱᱟ᱾
- p10 −$440
- p25 −$280
- ᱢᱤᱰᱤᱭᱟᱱ −$140
- p75 +$0
- p90 +$140
ᱢᱚᱱ ᱨᱮᱭᱟᱜ ᱵᱷᱟᱵᱱᱟ ᱪᱮᱫᱟᱜ ᱵᱷᱩᱞ ᱦᱩᱭᱩᱜ-ᱟ
ᱦᱚᱲ ᱫᱚ ᱵᱷᱟᱵᱱᱟ ᱠᱚ ᱛᱟᱦᱮᱸᱱᱟ ᱡᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱫᱚ ᱞᱚᱜᱚᱱ ᱧᱮᱞᱚᱜ-ᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ 2.70% ᱫᱚ ᱟᱹᱰᱤ ᱵᱟᱹᱲᱛᱤ ᱞᱮᱠᱟ ᱟᱹᱭᱠᱟᱹᱣᱚᱜ-ᱟ; ᱟᱨ ᱩᱭᱦᱟᱹᱨ ᱠᱚ ᱡᱮ ᱡᱮᱞᱮᱧ ᱫᱟᱣ ᱠᱚ “ᱥᱚᱢᱟᱱ ᱦᱩᱭᱩᱜ-ᱟ”, ᱪᱮᱫᱟᱜ ᱥᱮ ᱢᱟᱨᱟᱝ ᱮᱞ ᱨᱮᱭᱟᱜ ᱱᱤᱭᱚᱢᱜᱚᱱᱤᱛᱢᱟᱨᱟᱝ ᱮᱞ ᱨᱮᱭᱟᱜ ᱱᱤᱭᱚᱢᱯᱚᱨᱚᱠᱷ ᱨᱮᱭᱟᱜ ᱮᱞ ᱵᱟᱲᱦᱟᱣ ᱞᱮᱠᱷᱟᱱ ᱟᱡᱟᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱴᱷᱮᱱ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱟᱣᱥᱚᱛ ᱫᱚ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ᱾ ᱵᱟᱨᱭᱟ ᱵᱷᱟᱵᱱᱟ ᱜᱮ ᱢᱟᱯ ᱵᱷᱩᱞ ᱠᱚ ᱵᱩᱡᱷᱟᱹᱣᱟ: ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱣᱮᱨᱤᱭᱮᱱᱥᱜᱚᱱᱤᱛᱣᱮᱨᱤᱭᱮᱱᱥᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱷᱮᱨᱟᱣ ᱨᱮᱡᱟᱞᱴ ᱛᱤᱱᱟᱹᱜ ᱯᱟᱥᱱᱟᱣᱚᱜ-ᱟ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱟᱯᱲᱟᱣ᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ ᱵᱟᱹᱲᱛᱤ, ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱟᱶ ᱛᱩᱞᱟᱹ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱫᱚ ᱦᱩᱰᱤᱧ ᱜᱮᱭᱟ (σ = 1 ᱭᱩᱱᱤᱴ, EV = 0.027 ᱥᱟᱶ), ᱚᱱᱟᱛᱮ ᱢᱤᱫ ᱥᱤᱜᱽᱢᱟ ᱞᱮᱠᱟᱛᱮ ᱧᱮᱞᱚᱜ ᱞᱟᱹᱜᱤᱫ (1/0.027)² ≈ 1,400 ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾ ᱟᱨ ᱟᱣᱥᱚᱛ ᱨᱮᱭᱟᱜ ᱥᱮᱴᱮᱨ ᱫᱚ ᱡᱚᱛᱚ ᱛᱟᱭᱚᱢ ᱛᱮ ᱵᱟᱝ ᱟᱹᱜᱩᱭᱟ; ᱚᱱᱟ ᱫᱚ ᱥᱮᱫᱟᱭ ᱨᱮᱭᱟᱜ ᱪᱮᱛᱟᱱ-ᱞᱟᱛᱟᱨ ᱜᱮ ᱦᱟᱞᱠᱟ ᱠᱚ ᱵᱮᱱᱟᱣᱟ᱾
ᱮᱴᱟᱜ ᱵᱟᱡᱤ ᱞᱟᱹᱜᱤᱫ ᱥᱮᱴᱮᱨ
ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱟᱹᱜᱤᱫ σ = 5.84, ᱚᱱᱟᱛᱮ ᱚᱱᱟ ᱜᱮ ᱦᱤᱥᱟᱹᱵ ᱫᱚ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱢᱤᱫ ᱥᱤᱜᱽᱢᱟ ᱥᱮᱴᱮᱨ ᱞᱟᱹᱜᱤᱫ (5.84/0.027)² ≈ 47,000 ᱜᱷᱩᱨᱟᱹᱣ ᱮᱢᱚᱜ-ᱟ᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱠᱷᱮᱞᱚᱸᱰ ᱫᱚ ᱟᱡᱟᱜ ᱨᱮᱠᱚᱨᱰ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱵᱷᱟᱜᱚ ᱠᱷᱚᱱ ᱵᱷᱮᱜᱟᱨ ᱵᱟᱝ ᱧᱮᱞ ᱠᱟᱛᱮ ᱟᱭᱢᱟ ᱥᱮᱨᱢᱟ ᱠᱷᱮᱞ ᱫᱟᱲᱮᱭᱟᱜ-ᱟᱭ, ᱟᱨ ᱚᱱᱟ ᱚᱠᱛᱚ ᱨᱮ ᱦᱚᱸ ᱩᱱᱤ ᱫᱚ ᱴᱷᱤᱠ ᱚᱱᱟ ᱜᱮ 2.70% ᱮ ᱮᱢ ᱮᱫᱟ ᱡᱟᱦᱟᱸ ᱫᱚ ᱟᱨᱟᱜ ᱠᱷᱮᱞᱚᱸᱰ ᱫᱚ ᱦᱟᱯᱛᱟ ᱠᱚ ᱵᱷᱤᱛᱤᱨ ᱮ ᱧᱮᱞ ᱧᱟᱢᱟ᱾
ᱥᱤᱥᱴᱮᱢ ᱯᱚᱨᱚᱠᱷ ᱞᱟᱹᱜᱤᱫ ᱢᱟᱱᱮ
ᱡᱟᱦᱟᱸᱭ ᱦᱚᱸ ᱡᱩᱫᱤ ᱢᱮᱱᱟᱜ-ᱟᱭ ᱡᱮ ᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱠᱟᱹᱢᱤᱭᱟ, ᱩᱱᱤ ᱫᱚ 10,000 ᱥᱮ ᱟᱨᱦᱚᱸ ᱵᱟᱹᱲᱛᱤ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱚᱞ ᱟᱠᱟᱱ ᱯᱚᱡᱤᱴᱤᱵᱷ ᱟᱣᱥᱚᱛ ᱥᱟᱶ ᱩᱫᱩᱜ ᱫᱟᱲᱮᱭᱟᱜ ᱞᱟᱹᱠᱛᱤᱭᱟᱭ᱾ 1,000 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮ ᱯᱚᱡᱤᱴᱤᱵᱷ ᱟᱣᱥᱚᱛ ᱫᱚ ᱱᱟᱞ ᱦᱟᱭᱯᱚᱛᱮᱥᱤᱥ ᱞᱟᱛᱟᱨ ᱨᱮ ᱢᱚᱬᱮ ᱫᱷᱟᱣ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ; 100 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱫᱚ ᱚᱱᱟ ᱠᱚᱢ ᱵᱮᱥᱤ ᱥᱤᱠᱟᱹ ᱩᱪᱷᱞᱟᱹᱣ ᱞᱮᱠᱟ᱾ ᱱᱚᱶᱟ ᱥᱟᱭᱤᱴ ᱨᱮᱭᱟᱜ ᱥᱤᱢᱩᱞᱮᱴᱚᱨ ᱠᱚ ᱫᱚ ᱟᱯᱮ ᱵᱟᱪᱷᱟᱣ ᱟᱠᱟᱫ ᱡᱮᱞᱮᱧ ᱨᱮᱭᱟᱜ 2,000 ᱥᱮᱥᱚᱱ ᱢᱤᱫ ᱥᱮᱠᱮᱱᱰ ᱨᱮ ᱠᱚ ᱪᱟᱞᱟᱣᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱡᱟᱦᱟᱱᱟᱜ ᱦᱚᱲ ᱨᱮᱭᱟᱜ ᱥᱟᱠᱷᱭᱤ ᱠᱷᱚᱱ ᱵᱟᱹᱲᱛᱤ ᱥᱟᱵᱩᱫ ᱠᱟᱱᱟ᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱟᱯᱮ ᱡᱟᱦᱟᱸ ᱞᱮᱠᱟ ᱠᱷᱮᱞᱟ ᱯᱮ, ᱫᱩᱦᱲᱟᱹ ᱞᱟᱵᱷ ᱨᱮ ᱥᱮᱴᱮᱨ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱡᱤᱨᱚ ᱥᱮᱫ ᱠᱚᱢᱚᱜ-ᱟ᱾ ᱡᱚᱛᱚ ᱫᱚ ᱵᱤᱱᱟᱹ ᱢᱩᱪᱟᱹᱫ ᱛᱮ ᱞᱟᱛᱟᱨ ᱥᱮᱫ ᱪᱟᱞᱟᱜ-ᱟ᱾
ᱵᱟᱝ᱾ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱟᱱᱮ ᱫᱚ ᱱᱚᱶᱟ ᱡᱮ ᱥᱮᱫᱟᱭ ᱨᱮᱭᱟᱜ ᱪᱮᱛᱟᱱ-ᱞᱟᱛᱟᱨ ᱫᱚ ᱢᱤᱫ ᱢᱟᱨᱟᱝ ᱱᱢᱩᱱᱟ ᱨᱮᱭᱟᱜ ᱦᱩᱰᱤᱧ ᱦᱟᱹᱴᱤᱧ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ᱾
ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱞᱟᱹᱜᱤᱫ, ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱯᱩᱨᱟᱹ ᱧᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢ ᱵᱮᱥᱤ 10,000᱾ ᱥᱴᱨᱮᱴ ᱚᱯ ᱞᱟᱹᱜᱤᱫ, ᱠᱚᱢ ᱵᱮᱥᱤ 50,000᱾
ᱜᱚᱱᱤᱛ ᱥᱟᱶ ᱨᱟᱹᱥᱠᱟᱹ
ᱱᱚᱶᱟ ᱠᱚ ᱯᱩᱭᱞᱩ ᱟᱯᱮ ᱛᱮ ᱠᱩᱨᱩᱢᱩᱴᱩ ᱯᱮ᱾ ᱢᱤᱫ ᱢᱤᱫ ᱥᱚᱢᱟᱫᱷᱟᱱ ᱫᱚ ᱩᱠᱩ ᱢᱮᱱᱟᱜ-ᱟ; ᱛᱮᱭᱟᱨ ᱦᱩᱭ ᱠᱟᱛᱮ ᱡᱷᱤᱡᱽ ᱯᱮ᱾
ᱵᱟᱨ ᱜᱟᱛᱮ ᱠᱤᱱ ᱱᱤᱭᱟᱭ ᱠᱷᱮᱞᱜᱚᱱᱤᱛᱱᱤᱭᱟᱭ ᱠᱷᱮᱞᱚᱠᱟ ᱠᱷᱮᱞ ᱨᱮ ᱡᱟᱦᱟᱸᱱ ᱥᱮᱫ ᱦᱚᱸ ᱵᱟᱲᱛᱤ ᱵᱟᱹᱱᱩᱜ-ᱟ: ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱡᱤᱨᱚ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ 20 ᱫᱟᱣ ᱠᱤᱱ ᱠᱷᱮᱞᱟ, ᱠᱚᱭᱮᱱ ᱴᱚᱥ ᱥᱮ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱩᱣᱟᱹᱲ ᱥᱟᱶ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱤᱨᱩᱫᱷ ᱦᱮᱸᱫᱮᱵᱟᱡᱤᱦᱮᱸᱫᱮ18 ᱦᱮᱸᱫᱮ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱱᱣᱟᱨ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →, ᱟᱨ ᱪᱟᱞᱟᱣ ᱞᱮᱠᱷᱟ ᱠᱤᱱ ᱫᱚᱦᱚᱭᱟ᱾ ᱡᱚᱛᱚᱭ ᱚᱠᱛᱟ ᱫᱟᱣ ᱦᱟᱹᱵᱤᱡ ᱞᱟᱦᱟ ᱨᱮ ᱛᱟᱦᱮᱸᱭᱟ ᱚᱱᱟ ᱞᱮᱠᱷᱟ ᱯᱮ (ᱵᱟᱨᱟᱵᱟᱨ ᱫᱚ ᱡᱟᱦᱟᱸᱭ ᱞᱟᱦᱟ ᱨᱮ ᱞᱟᱦᱟ ᱛᱟᱦᱮᱸᱠᱟᱱᱟ ᱩᱱᱤᱭᱟᱜ ᱞᱮᱠᱷᱟᱚᱜ-ᱟ)᱾ ᱚᱠᱟ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱵᱮᱥᱤ: ᱞᱟᱦᱟ ᱫᱚ 10 ᱫᱟᱣ ᱨᱮ 10 ᱦᱟᱹᱴᱤᱧᱚᱜ-ᱟ, ᱥᱮ ᱢᱤᱫ ᱜᱟᱛᱮ ᱡᱚᱛᱚ 20 ᱨᱮ ᱞᱟᱦᱟ ᱨᱮ ᱛᱟᱦᱮᱸᱭᱟ?
ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ
ᱛᱮᱞᱟ ᱢᱤᱫ ᱜᱟᱛᱮ ᱡᱚᱛᱚ 20 ᱫᱟᱣ ᱞᱟᱦᱟ ᱨᱮ ᱛᱟᱦᱮᱸ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱟᱹᱰᱤ ᱵᱮᱥᱤ: 35.2%, ᱡᱟᱦᱟᱸᱭ ᱜᱟᱛᱮ ᱦᱚᱸ ᱞᱮᱠᱷᱟ ᱠᱟᱛᱮ, ᱥᱚᱢᱟᱱ 10 ᱨᱮ 10 ᱨᱮᱭᱟᱜ 6.1% ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣ ᱠᱟᱛᱮ᱾
ᱱᱤᱭᱟᱭ ᱪᱟᱞᱟᱣ ᱞᱮᱠᱷᱟ 2k ᱫᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱨᱟᱵᱟᱨ ᱛᱟᱦᱮᱸ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ u = C(2k, k)/2²ᵏ: 10 ᱫᱟᱣ ᱛᱟᱭᱚᱢ 0.246 ᱟᱨ 20 ᱛᱟᱭᱚᱢ 0.176᱾ ᱢᱤᱫ ᱢᱟᱨᱮ ᱨᱮᱡᱟᱞᱴ, ᱟᱨᱠ-ᱥᱟᱭᱤᱱ ᱱᱤᱭᱚᱢ, ᱢᱮᱱᱟᱭ ᱡᱮ ᱢᱤᱫ ᱧᱩᱛᱩᱢ ᱟᱠᱟᱱ ᱜᱟᱛᱮ 2n ᱫᱟᱣ ᱠᱷᱚᱱ ᱴᱷᱤᱠ 2k ᱫᱟᱣ ᱞᱟᱦᱟ ᱨᱮ ᱛᱟᱦᱮᱸ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ u(2k) × u(2n − 2k)᱾
ᱡᱚᱛᱚ 20 ᱞᱟᱦᱟ ᱨᱮ: ᱡᱚᱛᱚ ᱜᱟᱛᱮ ᱞᱟᱹᱜᱤᱫ u(20) × u(0) = 0.176, ᱡᱟᱦᱟᱸᱭ ᱦᱚᱸ ᱞᱟᱹᱜᱤᱫ 35.2%᱾ ᱥᱚᱢᱟᱱ ᱦᱟᱹᱴᱤᱧ: u(10) × u(10) = 0.246² = 6.1%, ᱡᱚᱛᱚ ᱠᱷᱚᱱ ᱠᱚᱢ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱦᱟᱹᱴᱤᱧ᱾
ᱚᱱᱟᱛᱮ ᱱᱤᱭᱟᱭ ᱠᱷᱮᱞ ᱨᱮ ᱞᱟᱦᱟ ᱫᱚ ᱠᱚᱢ ᱜᱮ ᱵᱚᱫᱚᱞᱚᱜ-ᱟ᱾ ᱡᱟᱦᱟᱸ ᱠᱷᱮᱞᱚᱸᱰ ᱜᱚᱴᱟ ᱟᱭᱩᱵ ᱞᱟᱦᱟ ᱨᱮ ᱥᱮ ᱛᱟᱭᱚᱢ ᱨᱮ ᱛᱟᱦᱮᱸᱠᱟᱱᱟᱭ, ᱩᱱᱤ ᱫᱚ ᱪᱮᱫ ᱦᱚᱸ ᱵᱷᱤᱱ ᱵᱟᱭ ᱧᱮᱞ ᱟᱠᱟᱫᱟ, ᱟᱨ ᱚᱱᱟ ᱫᱚ ᱪᱟᱠᱟ ᱥᱮ ᱫᱟᱠᱷᱭᱟᱹ ᱵᱟᱵᱚᱛ ᱪᱮᱫ ᱦᱚᱸ ᱵᱟᱝ ᱢᱮᱱᱟ᱾ ᱮᱯᱥᱴᱟᱭᱤᱱ (Epstein, 2013) ᱡᱮᱞᱮᱧ ᱠᱷᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱚᱱᱟ ᱜᱮ ᱱᱤᱭᱚᱢ ᱮ ᱮᱢ ᱟᱠᱟᱫᱟ: ᱟᱫᱷᱟ ᱚᱠᱛᱚ ᱵᱷᱟᱜᱽ ᱢᱮᱱᱟᱜ ᱫᱷᱟᱨᱮ ᱠᱷᱮᱞ ᱨᱮᱭᱟᱜ 85% ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱚᱠᱛᱚ ᱞᱟᱦᱟ ᱨᱮ ᱛᱟᱦᱮᱸᱭᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱟᱣᱥᱚᱛ ᱫᱚ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ᱾ ᱡᱚᱛᱚ ᱫᱚ ᱥᱟᱹᱝᱜᱤᱧ ᱜᱮ ᱪᱟᱞᱟᱜ-ᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.