ꯃꯇꯝ ꯁꯥꯡꯅ ꯅꯛꯅꯕ: ꯔꯨꯂꯦꯠꯇ ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝ
ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ −2.70%ꯗ ꯀꯔꯝꯅ ꯅꯛꯊꯔꯀꯄꯒꯦ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯅ ꯑꯩꯈꯣꯌꯅ ꯈꯜꯂꯤꯕꯗꯒꯤ ꯀꯔꯤꯒꯤ ꯃꯇꯝ ꯍꯦꯟꯅ ꯆꯪꯕꯒꯦ꯫
ꯁ꯭ꯄꯤꯟ ꯍꯦꯟꯒꯠꯂꯛꯄꯒꯥ ꯂꯣꯌꯅꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯃꯥꯡꯕ ꯑꯦꯚꯔꯦꯖ ꯁꯦꯜ ꯑꯁꯤ −1/37ꯗ ꯅꯛꯊꯔꯀꯏ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯒꯤ ꯁ꯭ꯞꯔꯦꯗ ꯑꯁꯤ 1/√N ꯒꯨꯝꯅ ꯍꯟꯊꯔꯛꯂꯤ꯫ ꯑꯉꯥꯡꯕꯗ ꯁ꯭ꯄꯤꯟ 1,000 ꯇꯥꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯀꯌꯥꯗ ꯃꯁꯤꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯗꯒꯤ ±3%ꯒꯤ ꯃꯅꯨꯡꯗ ꯂꯩ꯫
ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝ
ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯆꯠꯂꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯗꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯅꯛꯊꯔꯀꯏ꯫ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯆꯞ ꯃꯥꯟꯅꯕ ꯁ꯭ꯄꯤꯟ N ꯇꯥꯔꯕꯥ ꯃꯇꯨꯡꯗ, ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯁꯤ −1/37 ꯑꯃꯁꯨꯡ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯃꯦꯊꯃꯦꯇꯤꯛꯁꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯚꯦꯌꯔꯤꯌꯦꯟꯁꯀꯤ ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯔꯨꯠ; ꯃꯍꯩ ꯑꯃꯅ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯗꯒꯤ ꯌꯥꯝꯅ ꯂꯥꯞꯄ ꯃꯑꯣꯡ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ 1/√N ꯑꯣꯏ꯫ N = 100 ꯗ ꯁ꯭ꯞꯔꯦꯗ ꯑꯁꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ 10% ꯑꯣꯏ, ꯃꯁꯤ 2.7% ꯁꯤꯒ꯭ꯅꯦꯂꯗꯒꯤ ꯑꯃꯨꯛ ꯃꯔꯤꯒꯤ ꯃꯅꯥꯛꯇ ꯆꯥꯎꯏ꯫ N = 1,000 ꯗ ꯃꯁꯤ 3.2% ꯑꯣꯏ, ꯁꯤꯒ꯭ꯅꯦꯜ ꯑꯗꯨꯒ ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯆꯞ ꯃꯥꯟꯅꯩ꯫ N = 10,000 ꯗ ꯃꯁꯤ 1% ꯑꯣꯏ, ꯑꯃꯁꯨꯡ ꯍꯥꯎꯁ ꯑꯦꯖ ꯑꯁꯤ ꯃꯌꯦꯛ ꯁꯦꯡꯅ ꯎꯕ ꯐꯪꯏ꯫ ꯁꯦꯁꯟ ꯑꯃꯗ ꯍꯥꯎꯁ ꯑꯦꯖ ꯎꯕ ꯐꯪꯗꯦ, ꯆꯍꯤ ꯑꯃꯗ ꯃꯁꯤ ꯌꯥꯝꯅꯥ ꯃꯌꯦꯛ ꯁꯦꯡꯏ꯫
ꯀꯔꯤ ꯅꯛꯊꯔꯀꯄꯒꯦ ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯅꯛꯊꯔꯀꯗꯕꯒꯦ
ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ ꯅꯛꯊꯔꯀꯏ꯫ ꯄꯨꯝꯅꯃꯛ ꯁꯦꯜ ꯑꯗꯨ ꯅꯛꯊꯔꯀꯗꯦ: N ꯍꯦꯟꯒꯠꯂꯛꯄꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯁꯤ ꯖꯤꯔꯣꯗꯒꯤ ꯍꯦꯟꯅ ꯂꯥꯞꯊꯣꯛꯂꯛꯏ, ꯐꯪꯒꯗꯕ ꯃꯑꯣꯡꯗ N ꯒꯤ 2.7% ꯃꯔꯥꯡ ꯀꯥꯏꯅ, ꯃꯁꯤꯒꯤ ꯃꯅꯥꯛꯇ √N ꯒꯤ ꯁ꯭ꯞꯔꯦꯗ ꯂꯩꯅꯥ꯫ $10 ꯗ ꯁ꯭ꯄꯤꯟ 10,000 ꯁꯥꯟꯈꯤꯕ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯥ $2,700 ꯃꯥꯡꯒꯅꯤ ꯍꯥꯌꯅ ꯊꯥꯖꯩ, ꯃꯁꯤꯗꯒꯤ $1,000 ꯍꯦꯟꯕ ꯅꯠꯔꯒ ꯍꯟꯕ꯫ ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯊꯣꯛꯄꯒꯤ ꯆꯠꯂꯤꯕ ꯁꯔꯨꯛ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯃꯃꯥꯡꯗꯒꯤ 48.65% ꯒꯤ ꯃꯅꯥꯛꯇ ꯂꯦꯞꯂꯦ; ꯆꯠꯂꯤꯕ ꯕꯦꯂꯦꯟꯁ ꯑꯗꯨꯗꯤ ꯀꯗꯥꯏꯗꯁꯨ ꯂꯦꯞꯂꯃꯗꯦ꯫
- p10 −$440
- p25 −$280
- ꯃꯤꯗꯤꯌꯥꯟ −$140
- p75 +$0
- p90 +$140
ꯈꯜꯂꯕ ꯑꯗꯨ ꯀꯔꯤꯒꯤ ꯑꯔꯥꯟꯕꯒꯦ
2.70% ꯍꯥꯌꯕꯁꯤ ꯌꯥꯝꯅꯥ ꯆꯥꯎꯕ ꯑꯣꯏꯅ ꯇꯥꯕꯅꯥ ꯃꯤꯁꯤꯡꯅ ꯍꯥꯎꯁ ꯑꯦꯖ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯊꯨꯅ ꯎꯕ ꯐꯪꯒꯅꯤ ꯍꯥꯌꯅ ꯈꯜꯂꯤ, ꯑꯃꯁꯨꯡ ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝꯅꯃꯦꯊꯃꯦꯇꯤꯛꯁꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝꯍꯣꯠꯅꯕꯒꯤ ꯃꯁꯤꯡ ꯍꯦꯅꯒꯠꯂꯀꯄꯒ ꯂꯣꯌꯅꯅ ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯑꯗꯨ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯗ ꯅꯛꯂꯛꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯦꯚꯔꯦꯖꯁꯤꯡ ꯅꯛꯊꯔꯀꯏ ꯍꯥꯌꯕꯅꯥ ꯁꯥꯡꯕ ꯁ꯭ꯇ꯭ꯔꯤꯛꯁꯤꯡ “ꯆꯞ ꯃꯥꯟꯅꯍꯟꯒꯅꯤ” ꯍꯥꯌꯅ ꯈꯜꯂꯤ꯫ ꯈꯜꯂꯕ ꯑꯅꯤ ꯑꯁꯤꯅ ꯆꯥꯡ ꯑꯗꯨ ꯑꯔꯥꯟꯅ ꯂꯧꯏ: ꯍꯥꯎꯁ ꯑꯦꯖ ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ ꯑꯃꯒꯤ ꯚꯦꯌꯔꯤꯌꯦꯟꯁꯀꯥꯃꯦꯊꯃꯦꯇꯤꯛꯁꯚꯦꯌꯔꯤꯌꯦꯟꯁꯃꯍꯩꯁꯤꯡ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯑꯀꯣꯌꯕꯗ ꯀꯌꯥ ꯁꯟꯗꯣꯛꯅ ꯂꯩꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯆꯥꯡ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯇ ꯋꯥꯡꯏ, ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯗ ꯅꯦꯝꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯥꯡꯗꯝꯅꯕꯗ ꯑꯄꯤꯛꯄꯅꯤ (σ = ꯌꯨꯅꯤꯠ 1, EV = 0.027), ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯁꯤ ꯁꯤꯒ꯭ꯃꯥ ꯑꯃꯗ ꯎꯕ ꯐꯪꯅꯕ (1/0.027)² ≈ 1,400 ꯁ꯭ꯄꯤꯟ ꯃꯊꯧ ꯇꯥꯏ꯫ ꯑꯃꯁꯨꯡ ꯑꯦꯚꯔꯦꯖ ꯅꯛꯊꯔꯛꯄ ꯑꯁꯤꯅ ꯄꯨꯝꯅꯃꯛ ꯁꯦꯜ ꯑꯗꯨ ꯍꯜꯂꯛꯍꯟꯗꯦ; ꯃꯁꯤꯅ ꯃꯃꯥꯡꯒꯤ ꯍꯣꯡꯂꯛ-ꯍꯣꯡꯊꯛꯁꯤꯡ ꯑꯗꯨ ꯌꯥꯎꯊꯣꯛꯍꯜꯂꯤ ꯈꯛꯇꯅꯤ꯫
ꯑꯇꯣꯞꯄ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯅꯛꯊꯔꯛꯄ
ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯒꯤꯗꯃꯛ σ = 5.84, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯇꯧ ꯑꯗꯨꯃꯛꯀꯤ ꯀꯦꯜꯀꯨꯂꯦꯁꯟꯅ ꯍꯥꯎꯁ ꯑꯦꯖ ꯑꯁꯤ ꯁꯤꯒ꯭ꯃꯥ ꯑꯃꯗ ꯌꯧꯅꯕ (5.84/0.027)² ≈ 47,000 ꯁ꯭ꯄꯤꯟ ꯄꯤꯔꯤ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯃꯁꯥꯒꯤ ꯔꯦꯀꯣꯔꯗꯇ ꯍꯥꯎꯁ ꯑꯦꯖ ꯑꯗꯨ ꯂꯥꯀꯀꯤ ꯃꯍꯩꯗꯒꯤ ꯈꯥꯌꯗꯣꯛꯇꯅ ꯆꯍꯤ ꯀꯌꯥ ꯁꯥꯟꯕ ꯌꯥꯏ, ꯑꯗꯨꯕꯨ ꯃꯍꯥꯛꯅ ꯍꯞꯇꯥ ꯀꯌꯥꯒꯤ ꯃꯅꯨꯡꯗ ꯃꯁꯤ ꯎꯕ ꯐꯪꯂꯤꯕ ꯑꯉꯥꯡꯕ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯗꯨꯒꯨꯝꯅ ꯆꯞ ꯆꯥꯅꯕ 2.70% ꯑꯗꯨꯃꯛ ꯄꯤꯔꯤ꯫
ꯁꯤꯁ꯭ꯇꯦꯝ ꯆꯥꯡꯌꯦꯡ ꯇꯧꯕꯗ ꯃꯁꯤꯒꯤ ꯃꯔꯣꯜ
ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯅ ꯊꯕꯛ ꯄꯥꯡꯊꯣꯀꯏ ꯍꯥꯌꯕ ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯅ ꯁ꯭ꯄꯤꯟ 10,000 ꯅꯠꯔꯒ ꯃꯁꯤꯗꯒꯤ ꯍꯦꯟꯕꯗ ꯏꯔꯝ ꯊꯃꯗꯨꯅ ꯄꯣꯖꯤꯇꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯑꯃꯥ ꯎꯠꯄ ꯉꯝꯒꯗꯕꯅꯤ꯫ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯇ ꯁ꯭ꯄꯤꯟ 1,000 ꯗ ꯄꯣꯖꯤꯇꯤꯕ ꯑꯦꯚꯔꯦꯖ ꯑꯃꯥ ꯐꯪꯕ ꯍꯥꯌꯕꯁꯤ ꯅꯜ ꯍꯥꯏꯄꯣꯊꯤꯁꯤꯁꯀꯤ ꯃꯈꯥꯗ ꯃꯉꯥꯗ ꯑꯃꯥ ꯊꯣꯛꯄ ꯊꯧꯗꯣꯛꯅꯤ; ꯁ꯭ꯄꯤꯟ 100 ꯗ ꯃꯁꯤ ꯌꯥꯝꯅꯥ ꯀꯌꯥꯗ ꯄꯥꯏꯁꯥ ꯑꯃꯥ ꯊꯥꯗꯣꯛꯄꯒꯨꯝꯕꯅꯤ꯫ ꯃꯁꯤꯒꯤ ꯁꯥꯏꯠꯇ ꯂꯩꯕ ꯁꯤꯃꯨꯂꯦꯇꯔꯁꯤꯡꯅ ꯅꯍꯥꯛꯅ ꯈꯅꯕ ꯃꯇꯝ ꯆꯥꯡꯒꯤ ꯁꯦꯁꯟ 2,000 ꯆꯦꯛꯀꯟꯗ ꯑꯃꯗ ꯆꯂꯥꯏ, ꯃꯁꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯤꯑꯣꯏ ꯑꯃꯒꯤ ꯋꯥꯐꯃꯗꯒꯤ ꯍꯦꯟꯅ ꯆꯥꯎꯕ ꯈꯨꯗꯝꯅꯤ꯫
ꯐꯣꯔꯃꯨꯂꯥ
ꯋꯥꯍꯪꯁꯤꯡ
ꯅꯍꯥꯛꯅ ꯁꯥꯟꯂꯤꯉꯩꯗ ꯑꯃꯨꯛ ꯍꯟꯅ ꯀꯥꯟꯅꯕ ꯐꯪꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯖꯤꯔꯣꯗ ꯍꯟꯊꯔꯛꯂꯤ꯫ ꯄꯨꯝꯅꯃꯛ ꯁꯦꯜ ꯑꯁꯤ ꯉꯝꯈꯩ ꯌꯥꯎꯗꯅ ꯃꯈꯥ ꯊꯥꯗꯔꯛꯂꯤ꯫
ꯅꯠꯇꯦ꯫ ꯃꯁꯤꯒꯤ ꯑꯔꯊꯗꯤ ꯃꯃꯥꯡꯒꯤ ꯍꯣꯡꯂꯛ-ꯍꯣꯡꯊꯛꯁꯤꯡ ꯑꯁꯤ ꯍꯦꯟꯅ ꯆꯥꯎꯕ ꯁꯦꯝꯄꯜ ꯑꯃꯒꯤ ꯑꯄꯤꯛꯄ ꯁꯔꯨꯛ ꯑꯃꯥ ꯑꯣꯏꯔꯛꯏ꯫
ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯀꯤꯗꯃꯛ, ꯍꯥꯎꯁ ꯑꯦꯖ ꯃꯌꯦꯛ ꯁꯦꯡꯅ ꯎꯕ ꯐꯪꯅꯕ 10,000 ꯃꯔꯥꯡ ꯀꯥꯏꯅ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯀꯤꯗꯃꯛ, 50,000 ꯃꯔꯥꯡ ꯀꯥꯏꯅ꯫
ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ
ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫
ꯃꯔꯨꯞ ꯑꯅꯤꯅ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯀꯅꯥꯒꯨꯝꯕ ꯃꯥꯏꯀꯩ ꯑꯃꯠꯇꯗ ꯑꯦꯖ ꯂꯩꯇꯕ ꯁꯥꯟꯅꯕ: ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯖꯤꯔꯣꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤ ꯔꯥꯎꯟꯗ 20 ꯁꯥꯟꯅꯩ, ꯀꯣꯏꯟ ꯊꯥꯗꯣꯛꯄ ꯅꯠꯔꯒꯥ ꯖꯤꯔꯣꯁꯤꯡꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯍꯜꯂꯛꯄ ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯑꯃꯨꯕꯕꯦꯠꯑꯃꯨꯕꯑꯃꯨꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯅꯣꯌꯥꯔ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯑꯃꯁꯨꯡ ꯆꯠꯂꯤꯕ ꯁ꯭ꯀꯣꯔ ꯊꯝꯃꯤ꯫ ꯃꯤ ꯈꯨꯗꯤꯡ ꯃꯥꯡꯗ ꯂꯩꯔꯤꯕ ꯔꯥꯎꯟꯗꯁꯤꯡ ꯃꯁꯤꯡ ꯊꯤꯕꯤꯌꯨ (ꯃꯥꯟꯅꯕ ꯑꯃꯥ ꯃꯃꯥꯡꯗ ꯃꯥꯡꯗ ꯂꯩꯔꯝꯕꯒꯤꯗꯃꯛ ꯊꯤꯏ)꯫ ꯀꯅꯥꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯍꯦꯟꯅ ꯂꯩ: ꯃꯥꯡꯗ ꯂꯩꯕ ꯑꯗꯨ ꯔꯥꯎꯟꯗ 10 ꯗꯒꯤ 10 ꯌꯦꯟꯅꯕ, ꯅꯠꯔꯒꯥ ꯃꯔꯨꯞ ꯑꯃꯅ 20 ꯄꯨꯝꯅꯃꯛꯇ ꯃꯥꯡꯗ ꯂꯩꯕ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯃꯔꯨꯞ ꯑꯃꯅ ꯔꯥꯎꯟꯗ 20 ꯄꯨꯝꯅꯃꯛꯇ ꯃꯥꯡꯗ ꯂꯩꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯌꯥꯝꯅꯥ ꯍꯦꯟꯅ ꯂꯩ: 35.2%, ꯀꯅꯥꯒꯨꯝꯕ ꯃꯔꯨꯞ ꯑꯃꯥ ꯊꯤꯔꯕꯗ, ꯆꯞ ꯃꯥꯟꯅꯕ 10 ꯗꯒꯤ 10 ꯒꯤ 6.1% ꯒꯥ ꯆꯥꯡꯗꯝꯂꯕꯗ꯫
ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯠꯂꯤꯕ ꯁ꯭ꯀꯣꯔ ꯑꯃꯥ ꯔꯥꯎꯟꯗ 2k ꯒꯤ ꯃꯇꯨꯡꯗ ꯆꯞ ꯃꯥꯟꯅꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ u = C(2k, k)/2²ᵏ: ꯔꯥꯎꯟꯗ 10 ꯒꯤ ꯃꯇꯨꯡꯗ 0.246 ꯑꯃꯁꯨꯡ 20 ꯒꯤ ꯃꯇꯨꯡꯗ 0.176꯫ ꯀ꯭ꯂꯥꯁꯤꯛ ꯃꯍꯩ ꯑꯃꯥ, ꯑꯥꯔꯛ-ꯁꯥꯏꯟ ꯅꯤꯌꯝ, ꯅ ꯍꯥꯌꯔꯤ ꯃꯃꯤꯡ ꯊꯣꯅꯈꯤꯕ ꯃꯔꯨꯞ ꯑꯃꯅ ꯔꯥꯎꯟꯗ 2n ꯒꯤ ꯃꯅꯨꯡꯗ ꯆꯨꯝꯅ 2k ꯃꯥꯡꯗ ꯂꯩꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ u(2k) × u(2n − 2k)꯫
20 ꯄꯨꯝꯅꯃꯛꯇ ꯃꯥꯡꯗ ꯂꯩꯕ: ꯃꯔꯨꯞ ꯈꯨꯗꯤꯡꯒꯤꯗꯃꯛ u(20) × u(0) = 0.176, ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯒꯤꯗꯃꯛ 35.2%꯫ ꯆꯞ ꯃꯥꯟꯅꯕ ꯌꯦꯟꯅꯕ: u(10) × u(10) = 0.246² = 6.1%, ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯍꯟꯊꯕ ꯌꯦꯟꯅꯕ꯫
ꯃꯔꯝ ꯑꯗꯨꯅ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯗ ꯃꯥꯡꯗ ꯂꯩꯕ ꯑꯗꯨ ꯌꯥꯝꯅꯥ ꯇꯞꯅ ꯍꯣꯡꯏ꯫ ꯅꯨꯡꯊꯤꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯗ ꯂꯩꯔꯝꯕ, ꯅꯠꯔꯒꯥ ꯃꯇꯨꯡꯗ ꯂꯩꯔꯝꯕ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯑꯉꯛꯄ ꯀꯔꯤꯁꯨ ꯎꯈꯤꯗꯦ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯅ ꯆꯛꯔ ꯅꯠꯔꯒꯥ ꯃꯁꯛ ꯂꯧꯁꯤꯡꯒꯤ ꯃꯔꯃꯗ ꯀꯔꯤꯁꯨ ꯍꯥꯌꯗꯦ꯫ Epstein (2013) ꯅ ꯍꯦꯟꯅ ꯁꯥꯡꯕ ꯁꯥꯟꯅꯕꯁꯤꯡꯒꯤꯗꯃꯛ ꯅꯤꯌꯝ ꯑꯗꯨꯃꯛ ꯄꯤꯔꯤ: ꯃꯇꯝ ꯌꯥꯝꯈꯥꯏꯗ ꯂꯥꯛ ꯐꯕ ꯃꯥꯏꯀꯩ ꯑꯗꯨ ꯁꯥꯟꯅꯕꯒꯤ 85% ꯗꯒꯤ ꯍꯦꯟꯅ ꯃꯥꯡꯗ ꯂꯩ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯑꯦꯚꯔꯦꯖ ꯑꯁꯤ ꯅꯛꯊꯔꯀꯏ꯫ ꯄꯨꯝꯅꯃꯛ ꯁꯦꯜ ꯑꯗꯨꯗꯤ ꯂꯥꯞꯊꯣꯛꯂꯛꯏ ꯈꯛꯇꯅꯤ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.