ꯁꯃꯁ꯭ꯌꯥ: ꯗꯖꯟ ꯑꯅꯤ ꯑꯃꯁꯨꯡ ꯆꯤꯞ ꯑꯃꯥ

ꯁꯃꯁ꯭ꯌꯥ

ꯅꯍꯥꯛꯅ ꯑꯍꯥꯅꯕ ꯗꯖꯟꯗꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → $10, ꯑꯅꯤꯁꯨꯕ ꯗꯖꯟꯗ $10 ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣꯗꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → $1 ꯊꯝꯂꯤ꯫ (a) ꯊꯣꯛꯄ ꯌꯥꯕ ꯃꯍꯩꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯁꯤꯡ ꯀꯔꯤꯅꯣ? (b) ꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯀꯌꯥꯅꯣ? (c) ꯖꯤꯔꯣꯒꯤ ꯆꯤꯞꯅꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯦꯠ ꯑꯗꯨ ꯐꯒꯠꯍꯜꯂꯤꯕꯔꯥ?

ꯁꯣꯜꯌꯨꯁꯟ (a) ꯑꯃꯁꯨꯡ (b)

ꯃꯍꯩꯁꯤꯡ: ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 1–24 ꯗ (ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 24): ꯗꯖꯟ ꯑꯃꯅ $20 ꯄꯤ, ꯑꯇꯣꯞꯄ ꯑꯗꯨꯅ $10 ꯃꯥꯡꯏ, ꯖꯤꯔꯣꯅ $1 ꯃꯥꯡꯏ: ꯅꯦꯠ +$9꯫ ꯕꯣꯜ 25–36 ꯗ (ꯄꯣꯀꯦꯠ 12): ꯗꯖꯟ ꯑꯅꯤ ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯊꯤꯕ: −$21꯫ ꯕꯣꯜ ꯖꯤꯔꯣꯗ (ꯄꯣꯀꯦꯠ 1): ꯗꯖꯟꯁꯤꯡꯅ $20 ꯃꯥꯡꯏ, ꯖꯤꯔꯣꯅ $35 ꯄꯤ: +$15꯫ EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57, $21 ꯊꯝꯂꯕꯗ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ: 2.70%꯫

ꯁꯣꯜꯌꯨꯁꯟ (c)

ꯖꯤꯔꯣꯒꯤ ꯆꯤꯞ ꯌꯥꯎꯗꯅ: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54, $20 ꯊꯝꯂꯕꯗ, ꯃꯁꯤꯁꯨ 2.70%꯫ ꯖꯤꯔꯣꯒꯤ ꯆꯤꯞꯅ −$20 ꯑꯣꯏꯕ ꯖꯤꯔꯣꯒꯤ ꯃꯍꯩ ꯑꯗꯨ +$15 ꯑꯣꯏꯍꯜꯂꯦ (37 ꯗ ꯑꯃꯨꯛ $35 ꯒꯤ ꯐꯒꯠꯂꯀꯄ, ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ $0.95 ꯒꯤ ꯃꯃꯜ) ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯁ꯭ꯄꯤꯟ 36 ꯗ $1 ꯃꯥꯡꯍꯜꯂꯦ (ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ $0.97 ꯒꯤ ꯃꯃꯜ)꯫ ꯅꯦꯠ ꯍꯣꯡꯂꯀꯄ: ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ −$0.03, ꯃꯁꯤ ꯍꯦꯟꯅ ꯊꯝꯂꯕ ꯗꯣꯂꯥꯔ ꯑꯗꯨꯒꯤ 2.70% ꯅꯤ꯫ ꯏꯟꯁꯨꯔꯦꯟꯁ ꯑꯁꯤꯒꯤ ꯃꯃꯜ ꯑꯇꯩ ꯄꯨꯝꯅꯃꯛꯒꯨꯝꯅ ꯆꯞ ꯆꯥꯅꯕꯅꯤ꯫

ꯃꯁꯤ ꯀꯔꯤꯒꯤ ꯄꯨꯝꯅꯃꯛꯇ ꯆꯠꯅꯕꯒꯦ

ꯐꯪꯒꯗꯕ ꯃꯃꯂꯁꯤꯡ ꯄꯨꯟꯁꯤꯅꯕ ꯌꯥꯏ꯫ ꯃꯇꯝ ꯑꯃꯗ ꯊꯝꯂꯕ ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯠꯀꯤ ꯁꯦꯠ ꯑꯃꯒꯤ EV ꯑꯁꯤ ꯁꯔꯨꯛ ꯈꯨꯗꯤꯡꯒꯤ EV ꯄꯨꯟꯁꯤꯅꯕꯒꯥ ꯆꯞ ꯃꯥꯟꯅꯩ, ꯃꯈꯣꯌ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯁꯥꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37 ꯑꯣꯏ꯫ ꯃꯔꯝ ꯑꯗꯨꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯄꯨꯟꯁꯤꯅꯕ ꯑꯃꯃꯛ ꯄꯨꯝꯅꯃꯛ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37 ꯑꯣꯏ꯫ ꯂꯦꯑꯥꯎꯠꯇꯈꯨꯠꯂꯥꯏꯂꯦꯑꯥꯎꯠꯇꯦꯕꯜꯗ ꯏꯔꯕ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯒ꯭ꯔꯤꯗ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯇꯦꯕꯜ, ꯐꯦꯜꯠ, ꯀ꯭ꯂꯣꯊ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯤꯞ ꯀꯌꯥ ꯊꯝꯂꯕꯁꯨ, ꯃꯁꯤꯗꯒꯤ ꯅꯥꯟꯊꯣꯀꯄ ꯉꯝꯕ ꯊꯝꯕꯒꯤ ꯃꯑꯣꯡ ꯑꯃꯠꯇ ꯂꯩꯇꯦ; ꯅꯍꯥꯛꯅ ꯊꯝꯕ ꯉꯝꯕ ꯀꯔꯤꯒꯨꯝꯕ ꯁꯦꯠ ꯑꯃꯒꯤꯗꯃꯛ ꯕꯦꯠ ꯁꯦꯝꯕꯒꯤ ꯈꯨꯠꯂꯥꯏꯅ ꯃꯁꯤ ꯁꯣꯏꯗꯅ ꯎꯠꯀꯅꯤ꯫ ꯄꯨꯟꯁꯤꯅꯕꯁꯤꯡꯅ ꯍꯣꯡꯍꯜꯂꯤꯕꯗꯤ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟ ꯑꯗꯨꯅꯤ: ꯀꯌꯥ ꯌꯥꯝꯅꯥ ꯃꯥꯏꯄꯥꯛꯀꯅꯤ, ꯀꯌꯥ ꯐꯪꯒꯅꯤ, ꯑꯃꯁꯨꯡ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯠꯇꯕ ꯐꯤꯚꯝ ꯑꯗꯨ ꯀꯌꯥ ꯐꯠꯇꯒꯅꯤ꯫

ꯍꯦꯟꯅ ꯀꯟꯕ ꯃꯇꯨꯡꯒꯤ ꯁꯃꯁ꯭ꯌꯥ

ꯃꯁꯤꯡ 37 ꯄꯨꯝꯅꯃꯛ ꯌꯥꯎꯕ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯄꯨꯟꯁꯤꯅꯕ ꯑꯃꯥ ꯊꯤꯕꯤꯌꯨ꯫ ꯗꯖꯟ ꯑꯍꯨꯝ (ꯈꯨꯗꯤꯡꯃꯛ $10) ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣꯗ $1: 1–36 ꯒꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯗ ꯅꯦꯠ −$1 (ꯗꯖꯟ ꯑꯃꯅ $20 ꯄꯤ, ꯑꯇꯣꯞꯄ ꯑꯅꯤꯅ $20 ꯃꯥꯡꯏ, ꯖꯤꯔꯣꯅ $1 ꯃꯥꯡꯏ), ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣꯗ ꯅꯦꯠ +$35 − $30 = +$5꯫ EV = (36 × (−1) + 5)/37 = −31/37, $31 ꯊꯝꯂꯕꯗ: 2.70%꯫ ꯅꯍꯥꯛꯅ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯑꯉꯀꯄ ꯐꯪꯂꯣꯏꯗꯕꯅꯤ ꯍꯥꯌꯕ ꯁꯣꯌꯗꯅ ꯁꯦꯝꯕ ꯌꯥꯏ, ꯑꯃꯁꯨꯡ ꯈꯨꯗꯣꯜ ꯑꯗꯨꯒꯤꯗꯃꯛ ꯅꯍꯥꯛꯅ ꯍꯧꯖꯤꯀꯁꯨ ꯃꯃꯜ ꯑꯗꯨꯃꯛ ꯄꯤꯔꯤ꯫

ꯐꯣꯔꯃꯨꯂꯥ

ꯋꯥꯍꯪꯁꯤꯡ