ᱱᱢᱩᱱᱟ ᱢᱟᱯ
ᱢᱤᱫ ᱫᱷᱟᱡᱽ ᱨᱮᱭᱟᱜ ᱢᱟᱱᱮ ᱧᱟᱢ ᱞᱟᱹᱜᱤᱫ ᱛᱤᱱᱟᱹᱜ ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤ᱾

ᱢᱤᱫ ᱠᱷᱟᱱᱟ 37 ᱠᱷᱚᱱ 1 ᱵᱚᱫᱚᱞ ᱨᱮ 30 ᱠᱷᱚᱱ 1 ᱫᱷᱟᱣ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ, ᱱᱚᱶᱟ ᱵᱤᱥᱣᱟᱥ ᱥᱟᱶ ᱧᱟᱢ ᱞᱟᱹᱜᱤᱫ ᱯᱟᱥᱤ 4,400 ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾ 35 ᱠᱷᱚᱱ 1 ᱨᱮᱭᱟᱜ ᱠᱷᱟᱱᱟ, ᱡᱟᱦᱟᱸ ᱥᱟᱹᱨᱤ ᱛᱮ ᱞᱟᱵᱷ ᱮᱢ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱚᱱᱟ ᱞᱟᱹᱜᱤᱫ ᱯᱟᱥᱤ 70,000 ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾
ᱪᱮᱫᱟᱜ ᱱᱚᱣᱟ ᱟᱭᱢᱟ
ᱥᱤᱜᱽᱱᱟᱞ, ᱢᱤᱫ ᱦᱟᱡᱟᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱛᱤᱱᱟᱹᱜ ᱜᱟᱱ ᱵᱟᱹᱲᱛᱤ ᱦᱤᱴ, ᱫᱚ √(n·p·(1−p)) ≈ √(n/37) ᱵᱟᱭᱤᱱᱚᱢᱤᱭᱟᱞ ᱦᱩᱞᱟᱹᱢ ᱥᱮᱫ ᱠᱷᱚᱱ ᱦᱩᱰᱤᱧ᱾ ᱦᱩᱞᱟᱹᱢ 1/√n ᱞᱮᱠᱟ ᱠᱚᱢᱚᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱵᱟᱝ ᱵᱟᱰᱟᱭ ᱛᱟᱦᱮᱸ ᱫᱚ ᱟᱫᱷᱟ ᱞᱟᱹᱜᱤᱫ ᱯᱩᱱ ᱫᱷᱟᱣ ᱵᱟᱹᱲᱛᱤ ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾ 1/30 ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱢᱤᱫ ᱦᱟᱡᱟᱨ ᱨᱮ 33 ᱫᱷᱟᱣ ᱦᱤᱴᱚᱜ-ᱟ, ᱟᱸᱫᱟᱡᱽ 27 ᱫᱷᱟᱣ ᱛᱩᱞᱟᱹ: ᱛᱩᱨᱩᱭ ᱵᱟᱹᱲᱛᱤ ᱦᱤᱴ, ᱟᱨ ᱚᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱜᱚᱱᱤᱛᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱣᱮᱨᱤᱭᱮᱱᱥ ᱨᱮᱭᱟᱜ ᱵᱚᱜᱚ ᱢᱩᱞ; ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱠᱷᱚᱱ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱥᱟᱦᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱯᱟᱥᱤ ᱢᱚᱬᱮ᱾ ᱢᱤᱫ ᱦᱟᱡᱟᱨ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱱᱢᱩᱱᱟ ᱫᱚ ᱱᱚᱣᱟ ᱵᱟᱨᱭᱟ ᱵᱷᱚᱨᱚᱥᱟ ᱥᱟᱶ ᱵᱟᱝ ᱟᱞᱟᱜ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱥᱟᱭᱤᱰ ᱯᱚᱨᱚᱠᱷ ᱞᱟᱹᱜᱤᱫ, 5% ᱞᱮᱵᱮᱞ ᱨᱮ ᱟᱨ 80% ᱫᱟᱲᱮ ᱥᱟᱶ, ᱞᱟᱹᱠᱛᱤ n ᱫᱚ ᱯᱟᱥᱤ ((1.645·√(p₀(1−p₀)) + 0.84·√(p₁(1−p₁))) / (p₁ − p₀))², ᱡᱟᱦᱟᱸ ᱨᱮ p₀ = 1/37 ᱟᱨ p₁ ᱫᱚ ᱥᱟᱱᱫᱮᱦ ᱦᱟᱨ᱾ ᱱᱚᱣᱟ ᱫᱚ ᱞᱟᱦᱟ ᱠᱷᱚᱱ ᱵᱟᱪᱷᱟᱣ ᱢᱤᱫ ᱠᱷᱟᱱᱟ ᱞᱟᱹᱜᱤᱫ ᱜᱮ ᱥᱟᱹᱨᱤ᱾ ᱡᱩᱫᱤ ᱟᱯᱮ ᱡᱚᱛᱚ 37 ᱠᱷᱟᱱᱟ ᱨᱮ ᱥᱟᱵ ᱠᱷᱚᱱ ᱜᱚᱨᱚᱢ ᱥᱮᱸᱫᱽᱨᱟ ᱠᱟᱱᱟ ᱯᱮ, ᱵᱷᱩᱞ-ᱯᱚᱡᱤᱴᱤᱵᱷ ᱦᱟᱨ ᱴᱷᱤᱠ ᱫᱚᱦᱚ ᱞᱟᱹᱜᱤᱫ ᱯᱟᱥᱤ ᱵᱟᱨ ᱠᱷᱚᱱ ᱯᱮ ᱫᱷᱟᱣ ᱜᱩᱬ ᱯᱮ᱾
ᱠᱟᱹᱢᱤ ᱨᱮᱭᱟᱜ ᱯᱟᱲᱦᱟᱣ
300 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱜᱚᱨᱚᱢ ᱮᱞᱵᱷᱨᱚᱢᱜᱚᱨᱚᱢ ᱮᱞᱱᱤᱛᱚᱜ ᱟᱸᱫᱟᱡᱽ ᱠᱷᱚᱱ ᱵᱟᱹᱲᱛᱤ ᱫᱷᱟᱣ ᱦᱤᱡᱩᱜ ᱟᱠᱟᱱ ᱮᱞ᱾ ᱴᱷᱤᱠ ᱪᱟᱠᱟ ᱨᱮ ᱱᱚᱶᱟ ᱪᱮᱫ ᱦᱚᱸ ᱞᱟᱦᱟ ᱠᱟᱛᱷᱟ ᱵᱟᱝ ᱮᱢᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱦᱩᱞᱟᱹᱢ ᱠᱟᱱᱟ᱾ 3,000 ᱛᱟᱭᱚᱢ ᱚᱱᱟ ᱫᱚ ᱚᱱᱟ ᱜᱮ ᱪᱟᱠᱟ ᱠᱷᱚᱱ ᱟᱨᱦᱚᱸ 3,000 ᱡᱟᱣᱨᱟ ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫ ᱠᱟᱨᱚᱬ᱾ 30,000 ᱛᱟᱭᱚᱢ ᱚᱱᱟ ᱫᱚ ᱦᱟᱛ ᱛᱮ ᱥᱟᱯᱲᱟᱣ ᱞᱟᱹᱜᱤᱫ ᱡᱚᱜ ᱪᱟᱠᱟ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾ ᱤᱛᱤᱦᱟᱹᱥ ᱨᱮ ᱡᱚᱛᱚ ᱚᱞ ᱟᱠᱟᱱ ᱵᱟᱭᱟᱥ ᱞᱟᱵᱷ ᱫᱚ ᱟᱭᱢᱟ ᱦᱟᱡᱟᱨ ᱫᱚᱦᱚ ᱟᱠᱟᱱ ᱜᱷᱩᱨᱟᱹᱣ ᱪᱮᱛᱟᱱ ᱛᱮ ᱵᱮᱱᱟᱣ ᱞᱮᱱᱟ, ᱟᱨ ᱥᱟᱱᱟᱢ ᱨᱮ ᱟᱭᱢᱟ ᱪᱟᱸᱫᱚ ᱞᱟᱜᱟᱣ ᱞᱮᱱᱟ᱾
ᱰᱟᱴᱟ ᱨᱮᱭᱟᱜ ᱜᱚᱱᱚᱝ
ᱢᱤᱫ ᱜᱷᱟᱸᱴᱟ ᱨᱮ 50 ᱜᱷᱩᱨᱟᱹᱣ ᱦᱤᱥᱟᱹᱵ ᱛᱮ, 10,000 ᱜᱷᱩᱨᱟᱹᱣ ᱫᱚ 200 ᱜᱷᱟᱸᱴᱟ ᱫᱚᱦᱚ ᱠᱟᱹᱢᱤ, ᱥᱮ ᱪᱷᱟᱯᱟ ᱤᱛᱤᱦᱟᱹᱥ ᱱᱚᱠᱚᱞ ᱨᱮ ᱟᱭᱢᱟ ᱦᱟᱯᱛᱟ᱾ ᱱᱚᱣᱟ ᱡᱚᱛᱚ ᱢᱤᱫ ᱪᱤᱱᱦᱟᱹ ᱟᱠᱟᱱ ᱪᱟᱠᱟ ᱵᱚᱦᱚᱜᱥᱟᱡ ᱥᱟᱢᱟᱱᱪᱟᱠᱟ ᱵᱚᱦᱚᱜᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱮᱞ ᱠᱚ ᱫᱚᱦᱚ ᱜᱷᱩᱨᱟᱹᱣᱚᱜ ᱦᱟᱹᱴᱤᱧ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱷᱚᱱ ᱦᱩᱭᱩᱜ ᱞᱟᱹᱠᱛᱤᱭᱟ, ᱡᱟᱦᱟᱸ ᱠᱮᱥᱤᱱᱳ ᱱᱚᱣᱟ ᱚᱠᱛᱚ ᱨᱮ ᱵᱟᱝ ᱜᱷᱩᱨᱟᱹᱣ ᱟᱠᱟᱫᱟ ᱥᱮ ᱱᱟᱣᱟ ᱯᱷᱨᱮᱴ ᱵᱟᱝ ᱞᱟᱜᱟᱣ ᱟᱠᱟᱫᱟ᱾ ᱥᱴᱮᱴᱤᱥᱴᱤᱠᱥ ᱫᱚ ᱵᱟᱝ, ᱱᱚᱣᱟ ᱜᱮ ᱠᱟᱨᱚᱬ ᱵᱟᱭᱟᱥ ᱠᱷᱮᱞ ᱫᱚ ᱵᱟᱹᱱᱩᱜ ᱠᱟᱱᱟ: ᱢᱟᱨᱟᱢᱚᱛ ᱪᱟᱠᱨᱟ ᱫᱚ ᱰᱟᱴᱟ ᱡᱟᱣᱨᱟ ᱪᱟᱠᱨᱟ ᱠᱷᱚᱱ ᱦᱩᱰᱤᱧ᱾
ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱞᱟᱹᱜᱤᱫ ᱱᱢᱩᱱᱟ ᱢᱟᱯ
ᱚᱱᱟ ᱜᱮ ᱦᱤᱥᱟᱹᱵ ᱢᱮᱱᱮᱫᱟ ᱡᱮ ᱢᱤᱫ ᱠᱷᱮᱞᱚᱸᱰ ᱟᱡᱟᱜ ᱨᱮᱡᱟᱞᱴ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤᱜᱚᱱᱤᱛᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱠᱷᱚᱱ ᱠᱮᱥᱤᱱᱳ ᱟᱣᱥᱚᱛ ᱛᱮ ᱫᱚᱦᱚᱭ ᱦᱟᱹᱴᱤᱧ: ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱨᱩᱞᱮᱴ ᱨᱮ 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱧᱮᱞ ᱞᱟᱹᱜᱤᱫ ᱛᱤᱱᱟᱹᱜ ᱚᱠᱛᱚ ᱞᱟᱹᱠᱛᱤᱭᱟ: ᱢᱤᱫ ᱥᱤᱜᱽᱢᱟ ᱞᱟᱹᱜᱤᱫ ᱯᱟᱥᱤ 1,400 ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱜᱷᱩᱨᱟᱹᱣ, ᱟᱨ ᱵᱟᱲᱛᱤ ᱯᱩᱨᱟᱹ ᱥᱟᱯᱷᱟ ᱧᱮᱞ ᱞᱟᱹᱜᱤᱫ 10,000᱾ ᱡᱟᱦᱟᱸᱭ ᱚᱱᱟ ᱠᱷᱚᱱ ᱠᱚᱢ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱠᱟᱹᱢᱤᱭᱟ ᱢᱮᱱ ᱠᱟᱱᱟᱭ, ᱩᱱᱤ ᱦᱩᱞᱟᱹᱢ ᱜᱮ ᱞᱟᱹᱭ ᱠᱟᱱᱟᱭ᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱠᱩᱠᱞᱤ ᱠᱚ
ᱠᱷᱟᱱᱟ ᱵᱚᱫᱚᱞ ᱨᱮ ᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟᱥᱮᱠᱴᱚᱨᱪᱟᱠᱟ ᱨᱮ ᱛᱟᱭᱚᱢ ᱛᱟᱭᱚᱢ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱜᱩᱞᱟᱹᱭ ᱦᱟᱹᱴᱤᱧ, ᱞᱮᱭᱟᱣᱴ ᱨᱮᱭᱟᱜ ᱜᱩᱴᱤ ᱠᱷᱚᱱ ᱟᱞᱟᱜ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱯᱚᱨᱚᱠᱷ ᱫᱚ ᱜᱚᱲᱚ ᱮᱢᱚᱜ-ᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱢᱤᱫ ᱥᱟᱡ ᱜᱚᱞᱚᱛ ᱟᱡᱟᱜ ᱟᱹᱰᱤ ᱛᱮ ᱢᱤᱫ ᱟᱨᱠ ᱨᱮ ᱟᱥᱚᱨ ᱮᱢᱟᱜ-ᱟ ᱟᱨ ᱥᱤᱜᱽᱱᱟᱞ ᱠᱷᱟᱱᱟ ᱠᱚ ᱨᱮ ᱡᱩᱲᱟᱹᱣᱚᱜ-ᱟ᱾ ᱢᱮᱱᱠᱷᱟᱱ ᱱᱚᱣᱟ ᱫᱚ ᱢᱟᱯ ᱨᱮᱭᱟᱜ ᱦᱟᱨ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱟ᱾
ᱦᱮᱸ, ᱡᱩᱫᱤ ᱪᱟᱠᱟ ᱵᱚᱦᱚᱜ ᱚᱱᱟ ᱜᱮ ᱠᱟᱱᱟ ᱟᱨ ᱥᱟᱨᱣᱤᱥ ᱵᱟᱝ ᱦᱩᱭ ᱟᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱵᱟᱰᱟᱭ ᱜᱮ ᱠᱷᱟᱹᱞᱤ ᱢᱩᱥᱠᱤᱞ᱾
ᱪᱟᱞᱟᱜ ᱞᱮᱠᱟ᱾ ᱱᱚᱣᱟ ᱨᱮᱭᱟᱜ ᱢᱟᱱᱮ ᱫᱚ ᱞᱟᱹᱭ ᱟᱠᱟᱱ ᱢᱟᱯ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱥᱟᱹᱨᱤ ᱵᱟᱭᱟᱥ ᱫᱚ ᱢᱚᱬᱮ ᱫᱷᱟᱣ ᱠᱷᱚᱱ ᱯᱩᱱ ᱫᱷᱟᱣ ᱧᱟᱢᱚᱜ-ᱟ᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ

ᱦᱩᱞᱟᱹᱢ 1/√n ᱞᱮᱠᱟ ᱠᱚᱢᱚᱜ-ᱟ᱾ ᱥᱚᱵᱚᱨ ᱫᱚ ᱟᱨᱦᱚᱸ ᱞᱚᱜᱚᱱ ᱠᱚᱢᱚᱜ-ᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Barnhart, R. T. Beating the Wheel.