ᱫᱟᱞᱟᱸᱵᱮᱨ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤ
ᱫᱟᱞᱟᱸᱵᱮᱨ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱫᱚ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱥᱮᱞᱮᱫ ᱮᱫᱟ ᱟᱨ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱚᱪᱚᱜ ᱮᱫᱟ᱾
ᱱᱚᱶᱟ ᱫᱚ ᱪᱟᱠᱟ ᱵᱟᱭ ᱦᱟᱨᱟᱣᱟ᱾ ᱱᱚᱶᱟ ᱫᱚ ᱵᱟᱰᱟᱭ ᱟᱠᱟᱱ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱᱥᱴᱨᱮᱴᱮᱡᱤᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱᱢᱟᱨᱮ ᱨᱮᱡᱟᱞᱴ ᱞᱮᱠᱟ ᱛᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱚᱫᱚᱞ ᱡᱟᱦᱟᱸᱱ ᱱᱤᱭᱚᱢ᱾ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱲᱦᱟᱣᱟ, ᱯᱚᱡᱤᱴᱤᱵᱷ ᱡᱤᱛ ᱛᱟᱭᱚᱢ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱚ ᱛᱮ ᱡᱟᱹᱥᱛᱤ ᱥᱚᱢᱟᱱ ᱜᱮᱭᱟ: ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱞᱟᱦᱟᱭ ᱞᱟᱦᱟᱭ ᱪᱮᱛᱟᱱ ᱥᱮᱫ ᱥᱟᱨᱮᱡᱚᱜ-ᱟ, ᱯᱩᱸᱡᱤ ᱜᱷᱟᱴᱛᱤ ᱛᱟᱞᱟ ᱢᱟᱯ ᱨᱮᱭᱟᱜ, ᱟᱨ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱫᱚ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱚᱜ-ᱟ᱾
ᱥᱤᱥᱴᱮᱢ ᱛᱮ ᱥᱮᱱ ᱯᱮ
ᱦᱟᱹᱱᱤ ᱫᱚ ᱢᱤᱫ ᱫᱷᱟᱯ ᱪᱮᱛᱟᱱ ᱛᱮ ᱥᱟᱦᱮᱫ ᱮᱫᱟ᱾ ᱡᱤᱛ ᱫᱚ ᱢᱤᱫ ᱫᱷᱟᱯ ᱛᱟᱭᱚᱢ ᱛᱮ ᱥᱟᱦᱮᱫ ᱮᱫᱟ᱾
ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱟᱨ ᱨᱮᱡᱟᱞᱴ ᱫᱚ ᱢᱩᱞ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱭᱩᱱᱤᱴ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ᱾
ᱫᱟᱞᱟᱸᱵᱮᱨ ᱨᱩᱞᱮᱴ ᱥᱤᱥᱴᱮᱢ, ᱫᱷᱟᱯ ᱫᱷᱟᱯ
ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱯᱮ᱾ ᱦᱟᱹᱱᱤ ᱞᱮᱠᱷᱟᱱ ᱫᱟᱨᱟᱭ ᱵᱟᱡᱤ ᱫᱚ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱢᱟᱨᱟᱝ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱡᱤᱛ ᱞᱮᱠᱷᱟᱱ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱦᱩᱰᱤᱧ, ᱢᱮᱱᱠᱷᱟᱱ ᱛᱤᱥ ᱦᱚᱸ ᱢᱤᱫ ᱠᱷᱚᱱ ᱠᱚᱢ ᱵᱟᱝ᱾ ᱚᱱᱟ ᱜᱮ ᱡᱚᱛᱚ᱾ ᱢᱤᱫ ᱫᱷᱮᱱᱠᱤ ᱩᱭᱦᱟᱹᱨ ᱯᱮ: ᱡᱚᱛᱚ ᱦᱟᱹᱱᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱢᱤᱫ ᱫᱷᱟᱯ ᱪᱮᱛᱟᱱ ᱥᱮᱫ ᱨᱚᱠᱟᱣ ᱮᱫᱟ ᱟᱨ ᱡᱚᱛᱚ ᱡᱤᱛ ᱚᱱᱟ ᱞᱟᱛᱟᱨ ᱨᱩᱣᱟᱹᱲ ᱮᱫᱟ᱾ ᱞᱟᱛᱟᱨ ᱨᱮᱭᱟᱜ ᱯᱚᱛᱭᱟᱣ ᱫᱚ ᱱᱚᱶᱟ ᱠᱟᱱᱟ ᱡᱮ ᱡᱤᱛ ᱟᱨ ᱦᱟᱹᱱᱤ ᱫᱚ ᱥᱚᱢᱟᱱ ᱦᱩᱭᱩᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱵᱮᱥ ᱨᱮ ᱨᱩᱣᱟᱹᱲᱚᱜ-ᱟ᱾ ᱞᱩᱵᱷᱟᱹᱣ ᱫᱚ ᱱᱚᱶᱟ ᱠᱟᱱᱟ ᱡᱮ ᱥᱟᱢᱟᱝ ᱥᱟᱢᱟᱝ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮ ᱢᱤᱫ ᱡᱤᱛ ᱟᱨ ᱢᱤᱫ ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱡᱚᱲᱟ ᱫᱚ ᱥᱩᱫᱽ +1 ᱭᱩᱱᱤᱴ ᱮᱢ ᱮᱫᱟ: 3 ᱦᱟᱹᱱᱤ, 4 ᱡᱤᱛ, ᱥᱩᱫᱽ +1᱾
ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱫᱚ ᱪᱮᱫ ᱞᱮᱠᱟ ᱧᱮᱞᱚᱜ-ᱟ?
ᱥᱚᱢᱟᱱ, ᱞᱟᱦᱟᱭ ᱞᱟᱦᱟᱭ ᱪᱮᱛᱟᱱ ᱥᱮᱫ ᱥᱟᱨᱮᱡᱚᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱥᱟᱶ᱾ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮ ᱦᱟᱹᱱᱤ ᱫᱚ ᱡᱤᱛ ᱠᱷᱚᱱ 19 ᱨᱮ 18 ᱞᱮᱠᱟᱛᱮ ᱵᱮᱥᱤ ᱦᱩᱭᱩᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱡᱮᱞᱮᱧ ᱥᱮᱥᱚᱱ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱪᱮᱛᱟᱱ ᱥᱮᱫ ᱥᱟᱨᱮᱡᱚᱜ-ᱟ᱾ ᱦᱟᱹᱱᱤ ᱚᱠᱛᱚ ᱨᱮ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱡᱟᱹᱥᱛᱤ ᱩᱥᱩᱞ, ᱟᱨ ᱡᱤᱛ ᱚᱠᱛᱚ ᱨᱮ ᱠᱚᱢ, ᱚᱱᱟᱛᱮ ᱦᱟᱹᱱᱤ ᱚᱠᱛᱚ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱡᱤᱛ ᱚᱠᱛᱚ ᱨᱮᱭᱟᱜ ᱟᱣᱥᱚᱛ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱜᱮᱭᱟ᱾ ᱥᱮᱥᱚᱱ ᱫᱚ ᱢᱟᱨᱴᱤᱝᱜᱮᱞᱥᱴᱨᱮᱴᱮᱡᱤᱢᱟᱨᱴᱤᱝᱜᱮᱞᱡᱚᱛᱚ ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ᱾ ᱱᱚᱶᱟ ᱪᱮᱫ ᱮ ᱠᱟᱹᱢᱤᱭᱟ ᱟᱨ ᱪᱮᱫ ᱵᱟᱭ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱦᱟᱹᱴᱤᱧ ᱨᱮ ᱧᱮᱞ ᱯᱮ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱷᱚᱱ ᱥᱚᱢᱟᱱ ᱜᱮᱭᱟ, ᱛᱟᱞᱟ ᱢᱟᱯ ᱨᱮᱭᱟᱜ ᱯᱩᱸᱡᱤ ᱜᱷᱟᱴᱛᱤᱴᱟᱠᱟᱯᱩᱸᱡᱤ ᱜᱷᱟᱴᱛᱤᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱵᱷᱤᱛᱤᱨ ᱨᱮ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮᱭᱟᱜ ᱪᱩᱴ ᱠᱷᱚᱱ ᱛᱟᱭᱚᱢ ᱨᱮᱭᱟᱜ ᱞᱟᱛᱟᱨ ᱦᱟᱹᱵᱤᱡ ᱧᱩᱨ᱾ ᱢᱮᱠᱥᱤᱢᱩᱢ ᱯᱩᱸᱡᱤ ᱜᱷᱟᱴᱛᱤ ᱫᱚ ᱚᱱᱟ ᱞᱮᱠᱟᱱ ᱡᱚᱛᱚ ᱠᱷᱚᱱ ᱢᱟᱨᱟᱝ ᱧᱩᱨ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱟᱶ ᱟᱨ ᱵᱩᱨᱩ ᱠᱷᱚᱱ ᱧᱩᱨ ᱵᱟᱹᱱᱩᱜ-ᱟ, ᱟᱨ ᱟᱣᱥᱚᱛ ᱛᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤᱥᱴᱨᱮᱴᱮᱡᱤᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱡᱚᱛᱚ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱱᱚᱶᱟ ᱥᱟᱶ ᱛᱩᱞᱟᱹᱣᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱷᱚᱱ ᱛᱤᱱᱟᱹᱜ ᱵᱮᱥᱤ ᱦᱟᱹᱱᱤ ᱮᱫᱟ ᱪᱮᱫᱟᱜ ᱥᱮ ᱟᱣᱥᱚᱛ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱮᱥᱤ ᱜᱮᱭᱟ᱾
- p10 −$500
- p25 −$500
- ᱢᱤᱰᱤᱭᱟᱱ −$500
- p75 −$500
- p90 −$500
ᱫᱟᱞᱟᱸᱵᱮᱨ ᱥᱤᱥᱴᱮᱢ ᱠᱟᱹᱢᱤᱭ-ᱟ ᱥᱮ?
ᱵᱟᱝ᱾ ᱥᱚᱢᱟᱱ ᱥᱮᱥᱚᱱ ᱫᱚ ᱡᱤᱛᱚᱜ-ᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱥᱮᱥᱚᱱ ᱠᱚ ᱥᱚᱢᱟᱱ ᱵᱟᱝ ᱛᱟᱦᱮᱸᱱᱟ᱾ ᱥᱟᱢᱟᱝ ᱥᱟᱢᱟᱝ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮ w ᱡᱤᱛ ᱟᱨ l ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱥᱩᱫᱽ ᱨᱮᱡᱟᱞᱴ ᱫᱚ w − l ᱭᱩᱱᱤᱴ ᱟᱨ ᱥᱤᱲᱦᱤ ᱨᱮ ᱟᱯᱮ ᱚᱠᱟ ᱨᱮ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱚᱱᱟ ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫ ᱥᱩᱫᱷᱨᱟᱹᱣ ᱠᱟᱱᱟ᱾ w = l ᱞᱮᱠᱷᱟᱱ ᱨᱮᱡᱟᱞᱴ ᱫᱚ ᱴᱷᱤᱠ +w ᱭᱩᱱᱤᱴ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱯᱚᱠᱟ ᱞᱟᱵᱷ ᱞᱮᱠᱟ ᱧᱮᱞᱚᱜ-ᱟ᱾ ᱯᱮᱸᱪ ᱫᱚ ᱱᱚᱶᱟ ᱠᱟᱱᱟ ᱡᱮ w = l ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱞᱚᱛ ᱵᱟᱝ ᱠᱟᱱᱟ: 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 18 ᱡᱤᱛ ᱟᱨ 19 ᱦᱟᱹᱱᱤ ᱟᱸᱫᱟᱡᱽ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱡᱩᱫᱤ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ, ᱢᱮᱱ ᱞᱮ, 8 ᱭᱩᱱᱤᱴ ᱦᱟᱹᱵᱤᱡ ᱪᱟᱲᱦᱟᱣ ᱟᱠᱟᱱᱟ, ᱢᱤᱫ ᱵᱟᱹᱲᱛᱤ ᱦᱟᱹᱱᱤ ᱫᱚ ᱵᱮᱱᱟᱣ ᱟᱠᱟᱱ ᱤᱨᱟᱹᱞ +1 ᱡᱚᱲᱟ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱠᱷᱚᱨᱚᱪᱚᱜ-ᱟ᱾ ᱟᱸᱫᱟᱡᱽ ᱫᱚ ᱡᱚᱛᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵᱴᱟᱠᱟᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱦᱤᱥᱟᱹᱵᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱟᱨᱵᱟᱝ ᱚᱠᱛᱚ ᱨᱮ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ, ᱫᱚᱦᱲᱟ ᱞᱟᱜᱟᱣ ᱡᱤᱛ ᱴᱟᱠᱟ ᱥᱮᱞᱮᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱦᱮᱱᱰᱮᱞ, ᱮᱠᱥᱚᱱ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ −1/37 ᱜᱮ ᱦᱩᱭᱩᱜ-ᱟ, ᱡᱮᱢᱚᱱ ᱦᱩᱭᱩᱜ ᱞᱟᱹᱠᱛᱤ᱾
ᱦᱩᱰᱤᱧ ᱥᱮᱥᱚᱱ ᱫᱚ ᱟᱡᱟᱜ ᱞᱮᱠᱟᱛᱮ ᱪᱮᱫᱟᱜ ᱡᱤᱛᱚᱜ-ᱟ?
ᱥᱚᱢᱟᱱ ᱦᱟᱹᱞᱚᱛ ᱫᱚ ᱡᱚᱛᱚ ᱥᱮᱥᱚᱱ ᱵᱟᱵᱚᱫ ᱢᱤᱫ ᱱᱤᱭᱚᱢ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱠᱟᱱᱟ᱾ ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱞᱮᱠᱷᱟ ᱠᱷᱚᱱ ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱞᱮᱠᱷᱟ ᱚᱪᱚᱜ ᱠᱟᱛᱮ ᱚᱱᱟ D ᱢᱮᱱ ᱞᱮ᱾ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱠᱷᱚᱱ ᱮᱦᱚᱵᱚᱜ N ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱥᱮᱥᱚᱱ ᱫᱚ (N − D²)/2 − D ᱭᱩᱱᱤᱴ ᱨᱮ ᱢᱩᱪᱟᱹᱫᱚᱜ-ᱟ, ᱡᱟᱦᱟᱸ ᱦᱟᱹᱵᱤᱡ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱨᱮᱭᱟᱜ ᱡᱟᱦᱟᱸᱱ ᱵᱟᱡᱤ ᱵᱟᱝ ᱡᱤᱛᱚᱜ-ᱟ (ᱚᱱᱟ ᱞᱮᱠᱟᱱ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱟᱨᱦᱚᱸ ᱞᱟᱛᱟᱨ ᱥᱮᱫ ᱥᱟᱨᱮᱡ ᱵᱟᱝ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ)᱾ D = 0 ᱞᱮᱠᱷᱟᱱ ᱚᱱᱟ ᱫᱚ +N/2, ᱪᱮᱛᱟᱱ ᱦᱟᱹᱴᱤᱧ ᱨᱮᱭᱟᱜ +w᱾ ᱡᱚᱛᱚ ᱵᱟᱹᱲᱛᱤ ᱦᱟᱹᱱᱤ ᱫᱚ ᱵᱚᱨᱜᱚ ᱞᱮᱠᱟᱛᱮ ᱞᱮᱠᱷᱟᱚᱜ-ᱟ: 100 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ D 4 ᱞᱮᱠᱷᱟᱱ ᱦᱚᱸ +38 ᱭᱩᱱᱤᱴ ᱛᱟᱦᱮᱸᱱᱟ, D 8 ᱞᱮᱠᱷᱟᱱ +10, ᱟᱨ D 10 ᱞᱮᱠᱷᱟᱱ −10᱾ ᱥᱟᱹᱜᱩᱱ ᱜᱮ D ᱫᱚ ᱡᱚᱦᱚᱢ √N ᱞᱮᱠᱟ ᱟᱥᱟᱨ ᱮᱫᱟ, 100 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱜᱮᱞ, ᱟᱨ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱵᱤᱱᱟᱹ ᱠᱷᱮᱞ ᱨᱮ ᱟᱹᱰᱤ ᱥᱚᱢᱟᱱ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱞᱟᱵᱷ ᱟᱨ ᱛᱤᱱᱟᱹᱜ ᱜᱟᱱ ᱮᱠᱷᱮᱨ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱱᱤ ᱫᱚ ᱴᱷᱤᱠ ᱠᱟᱴᱟᱣᱚᱜ-ᱟ᱾ ᱡᱤᱨᱚ ᱫᱚ ᱟᱣᱥᱚᱛ ᱛᱮ ᱡᱚᱛᱚ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱵᱟᱹᱲᱛᱤ ᱦᱟᱹᱱᱤ ᱥᱮᱞᱮᱫ ᱮᱫᱟ, ᱟᱨ D ᱫᱚ ᱵᱚᱨᱜᱚ ᱦᱩᱭ ᱠᱟᱛᱮ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱨᱚᱪ ᱫᱚ ᱥᱮᱥᱚᱱ ᱠᱷᱚᱱ ᱞᱚᱜᱚᱱ ᱵᱟᱲᱦᱟᱣᱚᱜ-ᱟ᱾ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱦᱟᱹᱵᱤᱡ ᱡᱟᱹᱥᱛᱤ ᱥᱮᱥᱚᱱ ᱫᱚ ᱞᱟᱵᱷ ᱥᱟᱶ ᱢᱩᱪᱟᱹᱫᱚᱜ-ᱟ; ᱟᱣᱥᱚᱛ ᱫᱚ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱝ, ᱟᱨ ᱛᱤᱱᱟᱹᱜ ᱥᱟᱭ ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱡᱟᱹᱥᱛᱤ ᱥᱮᱥᱚᱱ ᱦᱚᱸ ᱦᱟᱹᱱᱤ ᱮᱫᱟ᱾
ᱱᱚᱶᱟ ᱩᱞᱴᱟᱹ ᱞᱮᱠᱷᱟᱱ ᱪᱮᱫ ᱦᱩᱭᱩᱜ-ᱟ?
ᱠᱚᱱᱴᱨᱟ-ᱫᱟᱞᱟᱸᱵᱮᱨ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱩᱞᱴᱟᱹ ᱫᱟᱞᱟᱸᱵᱮᱨ ᱦᱚᱸ ᱢᱮᱛᱟᱜ-ᱟ, ᱫᱚ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱥᱮᱞᱮᱫ ᱮᱫᱟ ᱟᱨ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱚᱪᱚᱜ ᱮᱫᱟ᱾ ᱱᱚᱶᱟ ᱫᱚ ᱢᱩᱞ ᱥᱤᱥᱴᱮᱢ ᱨᱮᱭᱟᱜ ᱴᱷᱤᱠ ᱟᱨᱥᱤ ᱠᱟᱱᱟ᱾ ᱡᱟᱦᱟᱸ ᱦᱟᱹᱵᱤᱡ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱨᱮᱭᱟᱜ ᱡᱟᱦᱟᱸᱱ ᱵᱟᱡᱤ ᱵᱟᱝ ᱦᱟᱹᱱᱤᱚᱜ-ᱟ, N ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱥᱮᱥᱚᱱ ᱫᱚ (D² − N)/2 + D ᱭᱩᱱᱤᱴ ᱨᱮ ᱢᱩᱪᱟᱹᱫᱚᱜ-ᱟ, ᱚᱸᱰᱮ D ᱫᱚ ᱱᱤᱛᱚᱜ ᱡᱤᱛ ᱠᱷᱚᱱ ᱦᱟᱹᱱᱤ ᱚᱪᱚᱜ ᱠᱟᱛᱮ ᱠᱟᱱᱟ᱾ ᱢᱤᱫ ᱥᱚᱢᱟᱱ ᱥᱮᱥᱚᱱ ᱫᱚ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱫᱷᱟ ᱭᱩᱱᱤᱴ ᱦᱟᱹᱱᱤ ᱮᱫᱟ, ᱟᱨ ᱦᱟᱹᱱᱤ ᱠᱷᱚᱱ ᱟᱹᱰᱤ ᱵᱮᱥᱤ ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱞᱟᱜᱟᱛᱟᱨ ᱜᱮ ᱞᱟᱵᱷ ᱮᱢ ᱮᱫᱟ᱾ ᱚᱱᱟᱛᱮ ᱡᱟᱹᱥᱛᱤ ᱥᱮᱥᱚᱱ ᱛᱤᱱᱟᱹᱜ ᱦᱟᱹᱱᱤ ᱮᱫᱟ ᱟᱨ ᱛᱤᱱᱟᱹᱜ ᱜᱟᱱ ᱟᱹᱰᱤ ᱡᱤᱛᱚᱜ-ᱟ, ᱢᱩᱞ ᱨᱮᱭᱟᱜ ᱫᱷᱟᱸᱪᱟ ᱨᱮᱭᱟᱜ ᱩᱞᱴᱟᱹ, ᱟᱨ ᱟᱣᱥᱚᱛ ᱫᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ ᱚᱱᱟ ᱜᱮ 2.70% ᱠᱟᱱᱟ᱾
ᱫᱟᱞᱟᱸᱵᱮᱨ ᱫᱚ ᱚᱠᱟᱭ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟᱭ?
ᱡᱟᱸ ᱞᱚ ᱨᱚᱸ ᱫᱟᱞᱟᱸᱵᱮᱨ (Jean le Rond d’Alembert), ᱜᱚᱱᱤᱛ ᱵᱤᱜᱭᱟᱱᱤ ᱟᱨ ᱟᱸᱥᱤᱠᱞᱚᱯᱮᱰᱤ (Encyclopédie) ᱨᱮᱭᱟᱜ ᱥᱟᱹᱜᱟᱹᱭ ᱥᱟᱯᱲᱟᱣᱤᱭᱟᱹ, 1754 ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱚᱱᱚᱞ ᱨᱮ ᱮ ᱢᱮᱛᱟᱫ ᱠᱟᱫᱟ ᱡᱮ ᱦᱮᱰ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱞᱟᱜᱟᱛᱟᱨ ᱛᱟᱭᱚᱢ ᱴᱮᱞ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱵᱮᱥᱤᱚᱜ-ᱟ᱾ ᱩᱱᱤ ᱵᱷᱩᱞ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟᱭ, ᱟᱨ ᱟᱡᱟᱜ ᱧᱩᱛᱩᱢ ᱵᱚᱦᱚᱜ ᱵᱷᱩᱞ ᱫᱚ ᱡᱩᱣᱟᱲᱤᱭᱟᱜ ᱵᱷᱩᱞ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱨᱩᱯ ᱠᱟᱱᱟ᱾ ᱨᱩᱞᱮᱴ ᱨᱮ ᱫᱟᱞᱟᱸᱵᱮᱨ ᱥᱤᱥᱴᱮᱢ ᱫᱚ ᱛᱟᱭᱚᱢ ᱛᱮ ᱩᱱᱤᱭᱟᱜ ᱧᱩᱛᱩᱢ ᱛᱮ ᱧᱩᱛᱩᱢ ᱮᱱᱟ, ᱚᱱᱟ ᱯᱚᱛᱭᱟᱣ ᱦᱟᱹᱴᱤᱧ ᱡᱩᱣᱟᱲᱤ ᱠᱚ ᱦᱚᱛᱮᱛᱮ᱾ ᱩᱱᱤ ᱫᱚ ᱵᱟᱭ ᱵᱮᱱᱟᱣ ᱞᱮᱫᱟ ᱟᱨ ᱟᱡ ᱞᱮᱠᱟᱛᱮ ᱵᱟᱭ ᱥᱟᱱᱟᱢ ᱞᱮᱫᱟ ᱦᱚᱸ᱾
ᱮᱴᱟᱜ ᱨᱩᱯ ᱢᱮᱱᱟᱜ-ᱟ ᱥᱮ?
ᱪᱮᱛᱟᱱ ᱨᱮᱭᱟᱜ ᱠᱚᱱᱴᱨᱟ-ᱫᱟᱞᱟᱸᱵᱮᱨ ᱫᱚ ᱢᱤᱫ ᱥᱚᱢᱟᱱ ᱯᱟᱨᱚᱞᱤᱥᱴᱨᱮᱴᱮᱡᱤᱯᱟᱨᱚᱞᱤᱯᱚᱡᱤᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ: ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱰᱚᱵᱚᱞ, ᱦᱟᱨᱟᱣ ᱛᱟᱭᱚᱢ ᱟᱨᱵᱟᱝ ᱞᱟᱜᱟᱛᱟᱨ ᱯᱮ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱫᱚᱦᱲᱟ ᱮᱛᱚᱦᱚᱵ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱩᱞᱴᱟᱹ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱞᱮᱠᱟ ᱪᱟᱞᱟᱜ-ᱟ᱾ ᱛᱤᱱᱟᱹᱜ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱵᱟᱨ ᱭᱩᱱᱤᱴ ᱥᱮᱞᱮᱫ ᱮᱫᱟ ᱟᱨ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱚᱪᱚᱜ ᱮᱫᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱤᱲᱦᱤ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱥᱮᱫ ᱠᱚᱲᱟ ᱵᱮᱱᱟᱣ ᱮᱫᱟ᱾ ᱡᱚᱛᱚ ᱨᱩᱯ ᱨᱮ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱵᱟᱡᱤ ᱨᱮ ᱚᱱᱟ ᱜᱮ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤᱜᱚᱱᱤᱛᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱜᱩᱬ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ; ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱟᱨᱵᱟᱝ ᱚᱠᱛᱚ ᱨᱮ ᱟᱣᱥᱚᱛ ᱛᱮ ᱦᱟᱨᱟᱣᱚᱜ ᱴᱟᱠᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱢᱮᱱᱟᱜ-ᱟ᱾
ᱥᱤᱢᱩᱞᱮᱴᱚᱨ · ᱫᱟᱞᱟᱸᱵᱮᱨ
$1,000 ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱠᱷᱚᱱ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ 2,000 ᱥᱮᱥᱚᱱ᱾
ᱢᱩᱞ ᱵᱟᱡᱤ $10 · ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹ $500 · ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱨᱮ 100 ᱜᱷᱩᱨᱟᱹᱣ
ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱞᱟᱜᱟᱛᱟᱨ ᱪᱮᱫ ᱥᱟᱦᱟᱣ ᱦᱤᱡᱩᱜ-ᱟ
ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ ᱪᱟᱠᱟ ᱨᱮ ᱢᱤᱫ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱫᱚ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 19 ᱫᱷᱟᱣ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ᱾ ᱢᱤᱫ ᱢᱤᱫ ᱛᱷᱟᱨ ᱫᱚ ᱩᱫᱩᱜ ᱮᱫᱟ ᱡᱮ ᱢᱤᱫ ᱜᱟᱱ ᱜᱷᱩᱨᱟᱹᱣ ᱡᱚᱛᱚ ᱦᱟᱨᱟᱣ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱪᱮᱫ, ᱟᱨ ᱡᱚᱛᱚ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱢᱩᱞ ᱵᱟᱡᱤ ᱥᱮᱞᱮᱫ ᱠᱟᱫ ᱢᱤᱫ ᱫᱟᱞᱟᱸᱵᱮᱨ ᱠᱷᱮᱞᱚᱸᱰ ᱚᱱᱟ ᱦᱟᱹᱵᱤᱡ ᱛᱤᱱᱟᱹ ᱦᱟᱨᱟᱣ ᱟᱠᱟᱫᱟᱭ᱾
| ᱞᱟᱜᱟᱛᱟᱨ ᱦᱟᱹᱱᱤ | ᱥᱚᱢᱵᱷᱟᱵᱱᱟ | ᱢᱚᱴᱟ ᱢᱩᱴᱤ 1 / | ᱱᱤᱛᱚᱜ ᱦᱟᱹᱵᱤᱡ ᱦᱟᱹᱱᱤ | ᱫᱟᱨᱟᱭ ᱵᱟᱡᱤ |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $3 |
| 3 | 13.5% | 7 | $6 | $4 |
| 4 | 7.0% | 14 | $10 | $5 |
| 5 | 3.6% | 28 | $15 | $6 |
| 6 | 1.8% | 55 | $21 | $7 |
| 7 | 0.94% | 106 | $28 | $8 |
| 8 | 0.48% | 207 | $36 | $9 |
| 9 | 0.25% | 403 | $45 | $10 |
| 10 | 0.13% | 784 | $55 | $11 |
| 11 | 0.065% | 1527 | $66 | $12 |
| 12 | 0.034% | 2974 | $78 | $13 |
| 13 | 0.017% | 5792 | $91 | $14 |
| 14 | 0.0089% | 11279 | $105 | $15 |
| 15 | 0.0046% | 21965 | $120 | $16 |
ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ 19/37 ᱠᱟᱱᱟ, ᱢᱤᱫ ᱢᱤᱫ ᱦᱟᱹᱱᱤ ᱨᱮ ᱟᱡ ᱥᱟᱶ ᱜᱩᱱ ᱠᱟᱛᱮ, ᱢᱤᱫ ᱛᱷᱤᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱚᱱ ᱞᱮᱠᱷᱟ ᱠᱟᱛᱮ᱾ ᱢᱤᱫ ᱡᱮᱞᱮᱧ ᱥᱮᱥᱚᱱ ᱨᱮ ᱟᱭᱢᱟ ᱜᱷᱩᱨᱟᱹᱣ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱟᱦᱟᱸ ᱠᱷᱚᱱ ᱱᱚᱶᱟ ᱞᱮᱠᱟᱱ ᱞᱟᱜᱟᱛᱟᱨ ᱮᱦᱚᱵ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱢᱤᱫ ᱟᱭᱩᱵ ᱨᱮ ᱱᱚᱣᱟ ᱫᱚ ᱢᱤᱫ ᱛᱷᱟᱨ ᱩᱫᱩᱜ ᱠᱷᱚᱱ ᱟᱹᱰᱤ ᱵᱮᱥᱤ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱱᱚᱶᱟ ᱨᱮ ᱵᱩᱨᱩ ᱠᱷᱚᱱ ᱧᱩᱨ ᱵᱟᱹᱱᱩᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱱᱚᱶᱟ ᱫᱚ ᱡᱟᱹᱥᱛᱤ ᱥᱚᱢᱟᱱ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱟᱱᱟ᱾ ᱱᱚᱶᱟ ᱫᱚ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱟᱡᱤ ᱠᱷᱚᱱ ᱠᱚᱢ ᱠᱷᱚᱨᱚᱪ ᱵᱟᱝ ᱠᱟᱱᱟ; ᱛᱤᱱᱟᱹᱜ ᱵᱮᱥᱤ ᱫᱟᱢ ᱜᱮᱭᱟ᱾
ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱴᱮᱵᱩᱞᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹᱦᱩᱠᱩᱢ ᱢᱮᱱᱟᱜ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱟᱨ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱵᱟᱡᱤ᱾ ᱵᱮᱥᱤ ᱥᱮ ᱵᱮᱥᱤ ᱥᱤᱢᱟᱹ ᱜᱮ ᱰᱚᱵᱚᱞ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱵᱚᱸᱫᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱥᱮ ᱟᱯᱮᱭᱟᱜ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤᱴᱟᱠᱟᱠᱷᱮᱞ ᱯᱩᱸᱡᱤᱠᱷᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱟᱞᱟᱜ ᱫᱚᱦᱚ ᱟᱠᱟᱱ ᱡᱚᱛᱚ ᱴᱟᱠᱟ᱾ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱥᱟᱢᱵᱷᱟᱞ ᱫᱚ ᱢᱮᱱᱮᱛ ᱢᱤᱫ ᱵᱟᱡᱤ ᱟᱨ ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱨᱮ ᱚᱱᱟ ᱠᱷᱚᱱ ᱛᱤᱱᱟᱹᱜ ᱡᱚᱠᱷᱤᱢ ᱨᱮ ᱫᱚᱦᱚᱭ ᱚᱱᱟ ᱴᱷᱟᱹᱣᱠᱟᱹ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱜᱮ᱾ ᱢᱤᱫ ᱡᱮᱞᱮᱧ ᱦᱟᱹᱱᱤ ᱥᱮᱥᱚᱱ ᱨᱮ ᱚᱱᱟ ᱞᱟᱜᱟᱛᱟᱨ ᱪᱟᱲᱦᱟᱣᱚᱜ-ᱟ᱾
ᱜᱚᱱᱤᱛ ᱥᱟᱶ ᱨᱟᱹᱥᱠᱟᱹ
ᱱᱚᱶᱟ ᱠᱚ ᱯᱩᱭᱞᱩ ᱟᱯᱮ ᱛᱮ ᱠᱩᱨᱩᱢᱩᱴᱩ ᱯᱮ᱾ ᱢᱤᱫ ᱢᱤᱫ ᱥᱚᱢᱟᱫᱷᱟᱱ ᱫᱚ ᱩᱠᱩ ᱢᱮᱱᱟᱜ-ᱟ; ᱛᱮᱭᱟᱨ ᱦᱩᱭ ᱠᱟᱛᱮ ᱡᱷᱤᱡᱽ ᱯᱮ᱾
ᱟᱯᱮ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ 50 ᱜᱷᱩᱨᱟᱹᱣ ᱦᱟᱹᱵᱤᱡ ᱫᱟᱞᱟᱸᱵᱮᱨ ᱯᱮ ᱠᱷᱮᱞᱟ, ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱷᱚᱱ ᱮᱦᱚᱵ ᱠᱟᱛᱮ, ᱟᱨ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱵᱟᱡᱤ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱝ ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ (ᱱᱚᱣᱟ ᱞᱮᱠᱟᱱ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱞᱟᱛᱟᱨ ᱥᱮᱫ ᱪᱟᱞᱟᱜ ᱞᱟᱹᱜᱤᱫ ᱡᱟᱭᱜᱟ ᱵᱟᱹᱱᱩᱜ-ᱟ)᱾ ᱟᱯᱮ 27 ᱦᱟᱹᱱᱤ ᱟᱨ 23 ᱡᱤᱛ ᱥᱟᱶ ᱢᱩᱪᱟᱹᱫᱟ ᱯᱮ᱾ ᱛᱤᱱᱟᱹᱜ ᱭᱩᱱᱤᱴ ᱞᱟᱵᱷ ᱥᱮ ᱦᱟᱹᱱᱤ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ ᱯᱮ? ᱟᱨ 29 ᱦᱟᱹᱱᱤ ᱟᱨ 21 ᱡᱤᱛ ᱥᱟᱶ?
ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ
ᱛᱮᱞᱟ 27 ᱦᱟᱹᱱᱤ ᱥᱟᱶ +13 ᱭᱩᱱᱤᱴ, 29 ᱥᱟᱶ −15 ᱭᱩᱱᱤᱴ᱾ ᱵᱟᱨ ᱤᱥᱤ ᱜᱮᱞ ᱠᱷᱚᱱ ᱵᱟᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱮᱴᱟᱜ ᱥᱮᱫ ᱪᱟᱞᱟᱜ ᱛᱮ 28 ᱭᱩᱱᱤᱴ ᱠᱷᱚᱨᱚᱪ ᱦᱩᱭᱩᱜ-ᱟ᱾
ᱦᱟᱹᱱᱤ ᱠᱷᱚᱱ ᱡᱤᱛ ᱤᱫᱤ ᱠᱟᱛᱮ ᱚᱱᱟ D ᱢᱮᱱ ᱯᱮ᱾ N ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱜᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱫᱚ (N − D²)/2 − D᱾ 27 ᱦᱟᱹᱱᱤ ᱟᱨ 23 ᱡᱤᱛ ᱥᱟᱶ, D = 4: (50 − 16)/2 − 4 = 17 − 4 = +13᱾ 29 ᱟᱨ 21 ᱥᱟᱶ, D = 8: (50 − 64)/2 − 8 = −7 − 8 = −15᱾
ᱱᱤᱭᱚᱢ ᱪᱮᱫᱟᱜ ᱴᱷᱤᱠ ᱠᱟᱱᱟ: ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱫᱚ ᱡᱚᱛᱚ ᱚᱠᱛᱚ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱥᱮᱞᱮᱫ ᱱᱤᱛ ᱦᱟᱹᱵᱤᱡ ᱦᱟᱹᱱᱤ ᱠᱚ ᱟᱨ ᱤᱫᱤ ᱱᱤᱛ ᱦᱟᱹᱵᱤᱡ ᱡᱤᱛ ᱠᱚ᱾ ᱡᱚᱛᱚ ᱦᱟᱹᱱᱤ ᱡᱟᱦᱟᱸ ᱛᱟᱭᱚᱢ ᱨᱮᱭᱟᱜ ᱡᱤᱛ ᱢᱮᱴᱟᱣᱟ ᱢᱤᱫ ᱡᱳᱲᱟ ᱮ ᱵᱮᱱᱟᱣᱟ, s ᱦᱟᱨᱟᱣ ᱟᱨ ᱛᱟᱭᱚᱢ s + 1 ᱡᱤᱛᱟᱹᱣ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱩᱫᱽ +1 ᱭᱩᱱᱤᱴ ᱮᱢᱟ, ᱪᱮᱛᱟᱱ ᱨᱮᱭᱟᱜ ᱛᱟᱹᱞᱤᱠᱟᱹ ᱡᱮᱞᱠᱟ ᱩᱫᱩᱜᱟ᱾ N ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ (N − D)/2 ᱱᱚᱣᱟ ᱞᱮᱠᱟᱱ ᱡᱳᱲᱟ ᱵᱮᱱᱟᱣᱚᱜ-ᱟ, ᱜᱚᱱᱚᱝ +(N − D)/2᱾ ᱵᱟᱹᱠᱤ D ᱦᱟᱹᱱᱤ ᱫᱚ ᱪᱮᱛᱟᱱ ᱥᱮᱫ ᱪᱟᱞᱟᱜ ᱚᱠᱛᱚ 1, 2 … D ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮ ᱞᱟᱜᱟᱣ ᱛᱟᱦᱮᱸᱱᱟ ᱟᱨ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱝ ᱢᱮᱴᱟᱣᱚᱜ ᱠᱟᱱᱟ; ᱩᱱᱠᱩᱣᱟᱜ ᱠᱷᱚᱨᱚᱪ 1 + 2 + … + D = D(D + 1)/2᱾ ᱥᱟᱶᱛᱮ: (N − D)/2 − D(D + 1)/2 = (N − D²)/2 − D᱾
ᱵᱚᱨᱜᱚ ᱜᱮ ᱜᱚᱴᱟ ᱠᱟᱛᱷᱟ ᱠᱟᱱᱟ᱾ ᱥᱚᱢᱟᱱ ᱥᱮᱥᱚᱱ ᱫᱚ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱫᱷᱟ ᱭᱩᱱᱤᱴ ᱮᱢᱟ, ᱟᱨ ᱥᱚᱢᱟᱱ ᱠᱷᱚᱱ ᱡᱚᱛᱚ ᱫᱷᱟᱯ ᱦᱟᱹᱥᱩᱨ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱨᱚᱪ ᱞᱟᱦᱟ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱱ ᱵᱮᱥᱤ᱾
ᱟᱯᱮ ᱟᱨᱟᱜ ᱨᱮ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱦᱟᱹᱵᱤᱡ ᱩᱞᱴᱟᱹ ᱫᱟᱞᱟᱸᱵᱮᱨ ᱯᱮ ᱠᱷᱮᱞᱟ, ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱠᱷᱚᱱ ᱮᱦᱚᱵ ᱠᱟᱛᱮ, ᱟᱨ ᱢᱤᱫ ᱭᱩᱱᱤᱴ ᱵᱟᱡᱤ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱝ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ᱾ ᱟᱯᱮ 52 ᱡᱤᱛ ᱟᱨ 48 ᱦᱟᱹᱱᱤ ᱥᱟᱶ ᱢᱩᱪᱟᱹᱫᱟ ᱯᱮ᱾ ᱟᱯᱮ ᱚᱠᱟ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ ᱯᱮ? ᱟᱨ 60 ᱡᱤᱛ ᱟᱨ 40 ᱦᱟᱹᱱᱤ ᱥᱟᱶ?
ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ
ᱛᱮᱞᱟ 52 ᱡᱤᱛ ᱥᱟᱶ −38 ᱭᱩᱱᱤᱴ, 60 ᱥᱟᱶ +170᱾ ᱡᱤᱛ ᱨᱮ ᱦᱩᱰᱤᱧ ᱞᱟᱦᱟ ᱦᱚᱸ ᱦᱟᱨᱟᱣᱚᱜ-ᱟ; ᱮᱠᱮᱞ ᱢᱟᱨᱟᱝ ᱞᱟᱦᱟ ᱜᱮ ᱵᱷᱩᱜᱛᱟᱱ ᱮᱢᱟ᱾
ᱡᱤᱛ ᱠᱷᱚᱱ ᱦᱟᱹᱱᱤ ᱤᱫᱤ ᱠᱟᱛᱮ ᱚᱱᱟ D ᱢᱮᱱ ᱯᱮ᱾ N ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱜᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱫᱚ (D² − N)/2 + D᱾
52 ᱡᱤᱛ ᱟᱨ 48 ᱦᱟᱹᱱᱤ: D = 4, ᱚᱱᱟᱛᱮ (16 − 100)/2 + 4 = −42 + 4 = −38᱾
60 ᱡᱤᱛ ᱟᱨ 40 ᱦᱟᱹᱱᱤ: D = 20, ᱚᱱᱟᱛᱮ (400 − 100)/2 + 20 = 150 + 20 = +170᱾
ᱪᱮᱫᱟᱜ: ᱡᱚᱛᱚ ᱡᱤᱛ ᱡᱟᱦᱟᱸ ᱛᱟᱭᱚᱢ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱱᱤ ᱢᱮᱴᱟᱣᱟ ᱢᱤᱫ ᱡᱳᱲᱟ ᱮ ᱵᱮᱱᱟᱣᱟ, s ᱨᱮ ᱡᱤᱛᱟᱹᱣ ᱟᱨ ᱛᱟᱭᱚᱢ s + 1 ᱨᱮ ᱦᱟᱨᱟᱣ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱩᱫᱽ −1 ᱮᱢᱟ᱾ ᱵᱟᱹᱠᱤ D ᱡᱤᱛ ᱫᱚ ᱪᱮᱛᱟᱱ ᱥᱮᱫ ᱪᱟᱞᱟᱜ ᱚᱠᱛᱚ 1, 2 … D ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮ ᱞᱟᱜᱟᱣ ᱛᱟᱦᱮᱸᱱᱟ ᱟᱨ ᱛᱤᱥ ᱦᱚᱸ ᱵᱟᱝ ᱢᱮᱴᱟᱣᱚᱜ-ᱟ; ᱩᱱᱠᱩ D(D + 1)/2 ᱠᱚ ᱟᱹᱜᱩᱭᱟ᱾ N ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ (N − D)/2 ᱡᱳᱲᱟ ᱵᱮᱱᱟᱣᱚᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱡᱚᱛᱚ ᱫᱚ D(D + 1)/2 − (N − D)/2 = (D² − N)/2 + D᱾
ᱱᱚᱣᱟ ᱫᱚ ᱢᱩᱞ ᱫᱟᱞᱟᱸᱵᱮᱨ ᱨᱮᱭᱟᱜ ᱱᱤᱭᱚᱢ ᱜᱮ ᱠᱟᱱᱟ, ᱪᱤᱱᱦᱟᱹ ᱠᱚ ᱩᱞᱴᱟᱹ ᱠᱟᱛᱮ: ᱚᱱᱰᱮ ᱥᱚᱢᱟᱱ ᱫᱚ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱫᱷᱟ ᱭᱩᱱᱤᱴ ᱡᱤᱛᱟᱹᱣᱟ ᱟᱨ ᱵᱟᱝ ᱥᱚᱢᱟᱱ ᱨᱮ ᱥᱟᱡᱟᱹ ᱧᱟᱢᱚᱜ-ᱟ; ᱱᱚᱰᱮ ᱥᱚᱢᱟᱱ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱨᱚᱪ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱫᱷᱟ ᱭᱩᱱᱤᱴ ᱟᱨ ᱵᱟᱝ ᱥᱚᱢᱟᱱ ᱮᱱᱟᱢ ᱧᱟᱢᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱢᱤᱫ ᱜᱚᱱᱤᱛ ᱵᱤᱜᱭᱟᱱᱤ ᱧᱩᱛᱩᱢ ᱛᱮ, ᱡᱟᱦᱟᱸᱭ ᱫᱚ ᱥᱤᱠᱟᱹ ᱵᱟᱵᱚᱫ ᱵᱷᱩᱞ ᱠᱟᱛᱷᱟ ᱮ ᱢᱮᱛᱟᱫ ᱠᱟᱫᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- RouletteDoc. Strategy description and examples.
- Roulette77. Strategy description and examples.
- d’Alembert, J. “Croix ou pile.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.