ᕉᓚᑦ: ᓈᓴᐃᓂᖅ · ᐱᒻᒪᕆᐅᔪᖅ ᐃᓱᒪᒋᔭᖅ · 7 ᒥᓂᑦ

ᕉᓚᑦ: ᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓ

ᕉᓚᑦᒥ ᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓ, ᐊᔾᔨᒌᙱᓐᓂᐅᑉᓈᓴᐃᓂᖅᐊᔾᔨᒌᙱᓐᓂᖅᐱᓐᓂᐅᔪᑦ ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᑕ ᐊᕙᓗᐊᓂ ᖃᓄᖅ ᓯᐊᒻᒪᒃᓯᒪᓂᖏᓐᓂᒃ ᓈᓴᐅᑎ. ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒥ ᐊᖏᔪᖅ, ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓂ ᐱᙳᐊᕈᑏᓐᓂ ᒥᑭᔪᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑐᖓᕕᖓ (√), ᐃᓱᓕᑦᑎᓂᐅᑉ ᓂᕆᐅᒋᔭᐅᔪᒥᑦ ᐊᑐᕐᓗᐊᖑᔪᖅ ᐅᖓᓯᓐᓂᖓ.

ᓇᐃᑦᑐᖅ ᑭᐅᔾᔪᑎ

$1-ᒧᑦ ᐱᙳᐊᕈᑎᒋᔭᐅᔪᒧᑦ σ 5.84-ᖑᔪᖅ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒧᑦ ᐊᒻᒪ 1.00 ᐊᐅᐸᓗᒃᑐᒧᑦ. ᐱᙳᐊᖅᑕᐅᓂᖓᓄᑦ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᓄᑦ ᑲᐃᕙᕐᓃᑦ ᐊᒥᓲᓂᖏᑕ ᑐᖓᕕᖓᓄᓪᓗ ᐊᒥᓲᓕᖅᑎᓪᓗᒍ.

ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎ
σ = 5.84
ᐊᐅᐸᓗᒃᑐᖅ
σ = 1.00
ᐊᖏᒡᓕᕐᓂᖓ
√N
±1σ
≈ 68% ᐱᙳᐊᖅᑕᐅᓂᖏᓐᓂᒃ

ᐊᑐᕐᓗᐊᖑᔪᖅ ᒪᓕᒐᖅ

ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐱᖓᓱᐃᓐᓇᐅᓂᖏᑕ ᒪᕐᕉᖏᑦ ᖃᓂᒋᔮᓂ ᓂᕆᐅᒋᔭᐅᔪᒥᑦ ᐊᑕᐅᓯᐅᑉ σ-ᐅᑉ ᐃᓗᐊᓂ ᐃᓱᓕᑉᐸᒃᑐᑦ ᐊᒻᒪ 95% ᒪᕐᕉᑉ ᐃᓗᐊᓂ. 100 ᐊᐅᐸᓗᒃᑐᒧᑦᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑲᐃᕙᕐᓂᓂ $10-ᒥ (ᓂᕆᐅᒋᔭᐅᔪᖅ −$27, σ = $100) ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐊᒥᓲᓂᖏᑦ −$127 ᐊᒻᒪ +$73 ᐊᑯᓐᓂᖓᓂ ᐃᓱᓕᑉᐸᒃᑐᑦ, ᖃᓂᒋᔮᓂᓗ ᑕᒪᕐᒥᒃ −$227 ᐊᒻᒪ +$173 ᐊᑯᓐᓂᖓᓂ. ᐃᓱᓕᑦᑎᓂᖅ ᑕᐃᒃᑯᐊ ᓯᓚᑖᓄᑦ ᓱᓇᒥᒃ ᓇᓗᓇᐃᖅᓯᙱᑦᑐᖅ, ᐱᙳᐊᖅᑕᐅᓂᖓ ᐊᑕᐅᓯᖅ ᖁᓖᓐᓂ ᒪᕐᕉᓐᓂ ᑕᒪᓐᓇ ᐱᑦᑕᕐᕕᐅᕙᒻᒪᑦ ᑭᓯᐊᓂ.

100 ᑲᐃᕙᕐᓃᑦ $10-ᒥ ᐊᐅᐸᓗᒃᑐᒧᑦᑭᒡᓕᖏᑦᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐃᓚᖏᑦ
1σ ᐃᓗᐊᓂ−$127-ᒥᑦ +$73-ᒧᑦ≈ 68%
2σ ᐃᓗᐊᓂ−$227-ᒥᑦ +$173-ᒧᑦ≈ 95%
3σ ᐃᓗᐊᓂ−$327-ᒥᑦ +$273-ᒧᑦ≈ 99.7%
ᑮᓇᐅᔭᒃᓴᖅᑐᑦ$0 ᐅᖓᑖᓄᑦ≈ 42%
$100 ᐅᕝᕙᓘᓐᓃᑦ ᐅᖓᑖᓄᑦ ᑮᓇᐅᔭᒃᓴᖅᑐᑦ+$100 ᐅᖓᑖᓄᑦ≈ 10%
ᐊᑐᕐᓗᐊᖑᔪᒥᒃ ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ ᖃᓂᒋᔮᖅᑐᖅ ᓈᓴᐃᓂᖅ. ᓱᓕᔪᑦ ᐊᕕᒃᓯᒪᓂᖏᑦ ᓯᕉᒧᑦ ᐊᑯᓂᐅᙱᑦᑐᒥᒃ ᓴᖑᓯᒪᔪᑦ.

ᓱᒻᒪᑦ √N

ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖅᓈᓴᐃᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᐊᕐᓕᒃᓗᒍ ᐱᙳᐊᕈᑏᑦ ᑲᑎᑕᐅᓂᖏᓐᓄᑦ; ᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐅᕝᕙᓘᓐᓃᑦ ᐱᕕᒃᓴᕐᒥ ᐊᓯᐅᔾᔨᓂᖅ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → N ᒪᓕᒃᓗᒍ ᐊᖏᒡᓕᕙᒃᑐᖅ; ᐊᕕᒃᓯᒪᓂᖓ √N ᒪᓕᒃᓗᒍ ᐊᖏᒡᓕᕙᒃᑐᖅ. N ᒥᑭᑉᐸᑦ ᐊᕕᒃᓯᒪᓂᖓ ᐊᖏᓂᖅᓴᐅᕙᒃᑐᖅ ᐊᒻᒪ ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᑮᓇᐅᔭᕐᒥᒃ ᒥᓯᒃᓯᓂᕐᒥᒃ ᐊᔾᔨᖃᖅᑐᑦ ᒥᑭᔪᒥᒃ ᓴᖑᓯᒪᓪᓗᑎᒃ. N ᐊᖏᑉᐸᑦ ᐊᓯᐅᔾᔨᓂᖅ ᐊᕕᒃᓯᒪᓂᕐᒥᒃ ᑭᖑᓪᓕᕆᓯᔪᖅ. ᐊᓯᔾᔨᕐᕕᖓ, ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖅ ᐊᑕᐅᓯᕐᒥᒃ ᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓᓂᒃᓈᓴᐃᓂᖅᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᓯᑭᐊᖅᑐᓂᖓ (√); ᐱᓐᓂᐅᑉ ᓂᕆᐅᒋᔭᐅᔪᒥᑦ ᐊᑐᐃᓐᓇᐅᒐᔪᒃᑐᖅ ᐅᖓᓯᑦᑎᒋᓂᖓ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᔾᔨᖃᓕᖅᑎᓪᓗᒍ, N = (σ/ᐃᓚᖓ)² = (1/0.027)² ≈ 1,370 ᑲᐃᕙᕐᓂᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ ᐊᒻᒪ (5.84/0.027)² ≈ 46,800 ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓄᑦᐱᙳᐊᕈᑎᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ, ᐊᑭᓕᐅᑎ 35:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →. ᑖᒃᑯᐊ ᓈᓴᐅᑏᑦ ᐊᑖᓃᓐᓂ ᐱᔪᓐᓇᕐᓂᖅ ᐃᓱᓕᑦᑎᔪᖅ; ᖁᓛᓃᓐᓂ, ᑳᓯᓅᑉ ᐃᓚᖓ ᐃᓱᓕᑦᑎᔪᖅ.

ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᐅᔾᔨᓂᖅ σ-ᒧᑦ ᐊᒥᓲᓕᖅᑎᑕᐅᓪᓗᓂ, $10 ᐊᐅᐸᓗᒃᑐᒧᑦEV / σ
10 ᑲᐃᕙᕐᓃᑦ
0.09
100 ᑲᐃᕙᕐᓃᑦ
0.27
1,000 ᑲᐃᕙᕐᓃᑦ
0.85
1,370 ᑲᐃᕙᕐᓃᑦ
1.00
10,000 ᑲᐃᕙᕐᓃᑦ
2.70
100,000 ᑲᐃᕙᕐᓃᑦ
8.54
EV / σ
04.258.54
ᐊᔾᔨᒌᙱᓐᓂᖓ 2 ᖃᓂᒋᔮᓂ ᐅᖓᑖᓄᑦ ᐊᓂᒍᖅᐸᑦ, ᑮᓇᐅᔭᒃᓴᖅᑐᑦ ᑐᓪᓕᖅᑐᑦ ᐱᑦᑕᕐᕕᐅᓐᖏᑦᑑᓕᖅᑐᑦ. ᑖᓐᓇ “ᑳᓯᓄ ᑕᒪᑦᑕᐃᓐᓇ ᐊᔪᒐᖅᑐᖅ” ᑐᑭᖓ ᐃᓘᓐᓇᖓ.

ᐊᑐᕐᓂᖓ

ᐱᙳᐊᖅᑕᐅᓂᖓ ᐊᔾᔨᐅᙱᑦᑐᒦᑦᑐᖅ ᖃᐅᔨᒋᐊᕈᕕᐅᒃ, (ᐃᓱᓕᑦᑎᓂᖅ − EV)/σ ᓈᓴᐃᓗᒍ. $10-ᒥᒃ ᐊᐅᐸᓗᒃᑐᒧᑦ ᐱᙳᐊᕈᑎᓕᐅᖅᑎ 100 ᑲᐃᕙᕐᓃᑦ ᑭᖑᓂᖏᓐᓂ +$150-ᒥ ᐃᓱᓕᑦᑐᖅ (150 + 27)/100 = 1.77σ-ᒥ ᐃᓂᖃᖅᑐᖅ, ᐊᑕᐅᓯᖅ 25-ᓂᑦ ᐃᓱᓕᑦᑎᓂᖅ: ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᐅᔪᖅ, ᑭᓯᐊᓂ ᑐᐊᕕᕐᓇᙱᑦᑐᖅ. ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓕᐅᖅᑎ ᐊᔾᔨᒌᒃᑐᒥ +$150-ᒥ 0.3σ-ᒥ ᐃᓂᖃᖅᑐᖅ: ᐊᑐᕐᓗᐊᖑᔪᖅ ᐅᓐᓄᖅ. ᐊᔾᔨᒌᒃᑐᖅ ᑮᓇᐅᔭᒃᑯᑦ ᐃᓱᓕᑦᑎᓂᖅ ᐊᔾᔨᒋᙱᑦᑐᓂ ᐱᙳᐊᕈᑎᓂ ᐊᔾᔨᒋᙱᑦᑐᓂᒃ ᑐᑭᖃᖅᑐᖅ.

ᐃᓚᖓᑕ ᐊᑐᕐᓗᐊᖑᔪᖅ ᑕᒻᒪᕐᓂᖓ

ᐊᔾᔨᒌᒃᑐᖅ ᓈᓴᐃᓂᖅ ᓇᓗᓇᐃᖅᓯᔪᖅ ᖃᑦᓯᓂᒃ ᑲᐃᕙᕐᓂᓂᒃ ᐱᔭᕆᐊᖃᕐᓂᖓᓂᒃ ᑳᓯᓅᑉ ᐃᓚᖓᓂᒃ ᓈᓴᐅᑎᓂ ᑕᑯᔪᓐᓇᕐᓂᕐᒧᑦ. ᑕᑯᔭᐅᔪᑦ ᐊᔪᒐᕐᓃᑦ ᐃᓚᖏᑕ ᐊᑐᕐᓗᐊᖑᔪᖅ ᑕᒻᒪᕐᓂᖓ √(p(1 − p)/N). ᐊᐅᐸᓗᒃᑐᒧᑦ N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. ᓈᒻᒪᒃᑐᖅ ᑮᓇᐅᔭᕐᒥᒃ ᒥᓯᒃᓯᓂᖅ ᐊᐅᐸᓗᒃᑐᕐᓗ ᐊᔾᔨᒋᙱᓐᓂᖏᑦ 1.35%-ᖑᔪᖅ, ᑕᐃᒪ 1,000 ᑲᐃᕙᕐᓃᑦ ᑭᖑᓂᖏᓐᓂ ᐊᔾᔨᒋᙱᓐᓂᖏᓐᓂᒃ ᖃᐅᔨᓪᓚᕆᒐᓱᓐᓂᐊᙱᓚᑎᑦ. 10,000 ᑭᖑᓂᖏᓐᓂ ᐊᑐᕐᓗᐊᖑᔪᖅ ᑕᒻᒪᕐᓂᖓ 0.5%-ᖑᔪᖅ ᐊᒻᒪ ᖃᐅᔨᔪᓐᓇᓕᕐᓂᐊᖅᑐᑎᑦ. ᑖᓐᓇ ᐱᓪᓗᒍ ᐊᒃᓴᓗᐊᑉ ᓴᖑᓯᒪᓂᖓᓂᒃ ᖃᐅᔨᓂᖅ ᐊᒥᓱᐊᓘᔪᓂᒃ ᑲᐃᕙᕐᓂᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ.

ᓴᖑᓯᒪᓂᖓᓂᒃ ᖃᐅᔨᒪᒋᐊᖃᖅᑐᖅ

ᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᓇᐃᑦᑐᒥ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᐅᑉ ᐃᓱᓕᑦᑎᓂᖏᑦ ᐊᑐᕐᓗᐊᖑᔪᒥᒃ ᐊᕕᒃᓯᒪᓂᕐᒥᑦ ᐅᖓᓯᒃᑐᐊᓘᔪᑦ: ᐱᙳᐊᖅᑕᐅᓂᖏᑦ ᐊᒥᓲᓂᖏᑦ −$10 ᑲᐃᕙᕐᓂᕐᒥ ᐊᔾᔨᐅᖃᑦᑕᖅᑐᑦ, ᐃᓛᓐᓂ +$350 ᐊᔪᒐᕐᓂᕐᒥᒃ. ±1σ ᒪᓕᒐᖅ ᐊᕕᒃᓯᒪᓂᖓᓂᒃ ᓱᓕᔪᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᖅ, ᑭᓯᐊᓂ ᐱᐅᓯᖓᓂᒃ ᓇᓗᓇᐃᖅᓯᓐᖏᑦᑑᒐᓗᐊᖅ N ᕼᐊᓐᑐᕆᑦ ᐊᒥᓱᓄᑦ ᑎᑭᑦᑎᓐᓇᒋᓂ. ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ ᐱᙳᐊᕈᑎᓄᑦᐱᙳᐊᕈᑎᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅ/ᕿᕐᓂᖅᑐᖅ, ᐊᕕᒃᑕᐅᔪᓐᓇᙱᑦᑐᖅ/ᐊᕕᒃᑕᐅᔪᓐᓇᖅᑐᖅ, ᐊᖏᔪᑦ/ᒥᑭᔪᑦ. 18 ᓈᓴᐅᑏᑦ, ᐊᑭᓕᐅᑎ 1:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑐᕐᓗᐊᖑᔪᒥᒃ ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ ᖃᓂᒋᔮᖅᑐᖅ ᓈᓴᐃᓂᖅ ᐱᐅᔪᖅ 30 ᖃᓂᒋᔮᓂ ᑲᐃᕙᕐᓃᑦ ᐱᒋᐊᖅᑎᓪᓗᒋᑦ.

ᓈᓴᐅᑎᓕᐅᕈᑎ

σ = √Var
σ_ᐱᙳᐊᖅᑕᐅᓂᖓ = σ · ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ · √N
z = (ᐃᓱᓕᑦᑎᓂᖅ − EV) / σ_ᐱᙳᐊᖅᑕᐅᓂᖓ

ᐊᐱᖅᑯᑏᑦ

2σ-ᒥ ᑮᓇᐅᔭᒃᓴᖅᑐᖅ ᐱᙳᐊᖅᑕᐅᓂᖓ ᐸᕐᓇᐅᑎ ᐱᐅᓂᖓᓂᒃ ᓇᓗᓇᐃᖅᓯᕙ?

ᓇᓗᓇᐃᖅᓯᔪᖅ ᐱᙳᐊᖅᑕᐅᓂᖏᓐᓂᒃ 40 ᖃᓂᒋᔮᓂ ᐱᙳᐊᖅᓯᒪᓂᕐᓂᒃ, ᐅᕝᕙᓘᓐᓃᑦ ᐊᑕᐅᓯᕐᒥ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᐅᔪᒥ ᓯᑕᒪᐃᓐᓇᐅᓂᖏᓐᓂ ᖁᓖᓐᓂ ᐃᓚᐅᓯᒪᓂᕐᓂᒃ. ᐱᙳᐊᖅᑲᓐᓂᕐᓗᒍ.

ᓱᒻᒪᑦ ᐊᑯᓂᐅᓂᖅᓴᒥ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᕋ ᓱᓕ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᕙ?

ᒥᑭᓕᖅᐸᓪᓕᐊᔪᒥᒃ ᐊᓯᑦᑐᖅᐸᓪᓕᐊᔪᖅ: ᐊᔾᔨᒌᒃᑎᑕᐅᔪᐅᑉ ᐊᑐᕐᓗᐊᖑᔪᖅ ᑕᒻᒪᕐᓂᖓ σ/√N. N = 10,000-ᒥ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ 1%-ᖓᑦ.

ᓈᓴᐃᓂᕐᒥᒃ ᐱᙳᐊᕐᓂᖅ

ᓯᕗᓪᓕᐅᓪᓗᓂ ᐃᓕᖕᓂᒃ ᐆᒃᑐᕐᓗᑎᑦ. ᑭᐅᔾᔪᑏᑦ ᐃᓗᓕᖏᑦ ᒪᑐᔭᐅᓯᒪᔪᑦ; ᐅᐸᒍᓐᓇᕈᕕᑦ ᒪᑐᐃᖅᓯᓗᒍ.

  1. ᐃᐅᕌᐸ ᐊᒃᓴᓗᐊᖓᓂ 100 ᑲᐃᕙᕐᓃᓐᓂ, ᐊᑦᔨᐅᑎᑮᓇᐅᔭᖅᐊᑦᔨᐅᑎᐸᕐᓇᐅᑎᐅᑉ ᐅᕝᕙᓘᓐᓃᑦ ᐱᙳᐊᖅᑎᐅᑉ ᑐᙵᕕᒋᔭᖓ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓ. ᐊᓯᑦᑐᖅᐸᓪᓕᐊᓂᐅᔪᑦ ᐊᑦᔨᐅᑎᓄᑦ ᓇᓗᓇᐃᖅᑕᐅᕙᒃᑐᑦ, ᑕᐃᒪ ᓇᓕᐊᓂᑐᐃᓐᓇᖅ ᐱᙳᐊᕐᕕᒻᒥ ᐊᑐᕈᓐᓇᖁᓪᓗᒋᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑕᐅᓯᖅ ᐊᐅᐸᓗᒃᑐᒧᑦᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓯᕗᓪᓕᐅᔪᖅ 51 ᐅᕝᕙᓘᓐᓃᑦ ᐅᖓᑖᓄᑦ ᐊᔪᒐᕐᓃᓐᓂ, ᐊᑦᔨᐅᑎᓗ ᐊᑕᐅᓯᖅ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᒥᐱᙳᐊᕈᑎᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ, ᐊᑭᓕᐅᑎ 35:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓯᕗᓪᓕᐅᔪᖅ ᓈᓴᐅᑎᖓ 3-ᕆᐊᖅᓗᒍ ᐅᖓᑖᓄᓘᓐᓃᑦ ᓴᖅᑭᑉᐸᑦ. ᖃᒻᒥᐅᑎᑐᑦ ᐊᔾᔨᓕᒃ ᐊᔾᔨᐅᓯᐊᖅ ᐊᑐᕐᓗᒍ ᒪᕐᕉᒃ ᐱᔪᓐᓇᕐᓃᒃ ᓇᓚᐅᑦᑖᕐᓗᒋᒃ, ᑕᐃᑦᓱᒪᓂᓗ ᑭᐅᔾᔪᑏᓐᓄᑦ ᓱᓕᓪᓚᕆᒃᑐᓄᑦ ᐊᔾᔨᒋᙱᑦᑐᖓᓗᒋᒃ.

    ᑭᐅᔾᔪᑎ ᑕᑯᓗᒍ

    ᑭᐅᔾᔪᑎ ᐊᐅᐸᓗᒃᑐᖅ: ᖃᒻᒥᐅᑎᑐᑦ ᐊᔾᔨᐅᓯᐊᖅ 35.6%-ᒥᒃ ᓴᖅᑭᑦᑎᔪᖅ ᓱᓕᓪᓚᕆᒃᑐᓗ ᑭᐅᔾᔪᑎ 35.5%. ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎ: ᖃᒻᒥᐅᑎᑐᑦ ᐊᔾᔨᐅᓯᐊᖅ 55.0%-ᒥᒃ ᓴᖅᑭᑦᑎᔪᖅ ᓱᓕᓪᓚᕆᒃᑐᓗ ᑭᐅᔾᔪᑎ 50.9%. ᓱᒃᑲᐃᑦᑐᖅ ᐱᐅᓯᖅ ᐊᐅᐸᓗᒃᑐᒧᑦ ᐱᓕᕆᐊᖅᑐᖅ ᓈᓴᐅᑎᒧᓪᓗ ᐊᑕᐅᓯᕐᒧᑦ ᑕᒻᒪᖅᑐᖅ.

    ᐊᐅᐸᓗᒃᑐᖅ: ᐊᔪᒐᕐᓃᑦ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ 100 × 18/37 = 48.6, ᐊᕕᒃᓯᒪᓂᖓ √(100 × 18/37 × 19/37) = 5.0. ᓯᕗᓪᓕᐅᓂᖅ 51 ᐅᕝᕙᓘᓐᓃᑦ ᐅᖓᑖᓄᑦ; ᕿᑎᐊ, 50.5, 0.37 ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᒥᑦ ᖁᓛᓂ, ᖃᒻᒥᐅᑎᑐᓪᓗ ᐊᔾᔨᐅᓯᐊᖅ 35.6%-ᒥᒃ ᑕᑦᓱᒪ ᖁᓛᓂ ᐃᓕᔪᖅ. 51, 52 … 100 ᐊᔪᒐᕐᓃᑦ ᓱᓕᓪᓚᕆᒃᑐᑦ ᐱᔪᓐᓇᕐᓂᖏᑦ ᑲᑎᓪᓗᒋᑦ 35.5%.

    ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎ: ᓴᖅᑭᓃᑦ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ 100/37 = 2.70, ᐊᕕᒃᓯᒪᓂᖓ √(100 × 1/37 × 36/37) = 1.62. ᐱᖓᓱᑦ ᐅᖓᑖᓄᓘᓐᓃᑦ ᓴᖅᑭᓃᑦ 2.5-ᒥᑦ ᖁᓛᓂ, 0.12 ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᒥᑦ ᐊᑖᓂ: 55.0% ᖃᒻᒥᐅᑎᑐᑦ ᐊᔾᔨᐅᓯᐊᕐᒥ. ᓱᓕᓪᓚᕆᒃ, 1 ᐲᖅᑕᐅᓪᓗᓂ 0, 1 2-ᓗ ᓴᖅᑭᓃᑦ ᐱᔪᓐᓇᕐᓂᖏᓐᓂᒃ, 6.5% + 17.9% + 24.7%, 50.9%-ᒥᒃ ᐊᓯᐅᖅᑕᐃᓕᔪᖅ.

    ᖃᒻᒥᐅᑎᑐᑦ ᐊᔾᔨᐅᓯᐊᖅ ᐊᒥᓱᓂᒃ ᓴᖅᑭᑦᑕᓂᒃ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᑉ ᒪᕐᕉᖕᓂ ᓴᓂᖏᓐᓂ ᐱᔭᕆᐊᖃᖅᑐᖅ. ᐊᐅᐸᓗᒃᑐᖅ 100 ᑲᐃᕙᕐᓃᑦ ᐊᓂᒍᖅᑎᓪᓗᒋᑦ ᐱᑕᖃᖅᑐᖅ; ᓈᓴᐅᑎ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ ᐱᖓᓱᓂᑦ ᒥᑭᓂᖅᓴᓂ ᓴᖅᑭᑦᑐᖅ ᐱᑕᖃᙱᑦᑐᖅ. ᐊᔾᔨᐅᓯᐊᖅ “ᓴᖅᑭᓂᖃᙱᑦᑐᒧᑦ” 8.7%-ᒥᒃ ᑐᓂᓯᔪᖅ, ᓱᓕᔪᖅ ᐱᔪᓐᓇᕐᓂᖅ 6.5% ᐊᓯᐊᓂ. ᑎᐃᓗ (Taylor, 2021) ᒪᕐᕉᓄᑦ ᐊᕕᒃᓯᒪᓂᖏᓐᓂᒃ (binomial) ᖃᒻᒥᐅᑎᑐᓪᓗ ᐊᔾᔨᐅᓯᐊᕐᒥᒃ ᓴᓂᓕᕇᑦᑎᔪᖅ ᐊᔾᔨᒋᔭᐅᔪᒥᒃ ᐱᐅᓯᖃᖅᓗᓂ.

ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ

ᐱᙳᐊᖅᑕᐅᓂᖓ ᐊᑕᐅᓯᖅ ᖁᓖᓐᓂ ᒪᕐᕉᓐᓂ ᒪᕐᕉᒃ ᓯᒡᒪᒃ ᓯᓚᑖᓂ ᐃᓱᓕᑉᐸᒃᑐᖅ. ᐃᓄᒃ ᑕᒪᑦᑕᐃᓐᓇ ᐱᑕᖃᖅᑐᖅ ᓴᓂᖓᓃᑦᑐᒥ.

ᐱᙳᐊᖅᑕᐅᓂᖓ ᐊᑕᐅᓯᖅ ᖁᓖᓐᓂ ᒪᕐᕉᓐᓂ ᒪᕐᕉᒃ ᓯᒡᒪᒃ ᓯᓚᑖᓂ ᐃᓱᓕᑉᐸᒃᑐᖅ. ᐃᓄᒃ ᑕᒪᑦᑕᐃᓐᓇ ᐱᑕᖃᖅᑐᖅ ᓴᓂᖓᓃᑦᑐᒥ.

ᐱᕝᕕᒋᔭᐅᔪᑦ

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3-ᖓ ᓴᖅᑭᑎᑕᐅᓂᖓ, 1968. ᐱᙳᐊᖅᑎᐅᑉ ᓱᕋᐃᓂᖓ, ᐃᓚᖓ XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. ᐃᓚᖓ 13, ᕉᓚᑦ.
  3. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
ᕿᒥᕐᕈᔭᐅᓚᐅᖅᑐᖅ 2026-09-28ᐊᔾᔨᐅᖅᑕᐅᑎ: ᐃᐅᕌᐸ, ᐊᑕᐅᓯᖅ ᓯᕉᖃᓄᖅ ᓈᓴᐃᓂᖅ ↗ᐱᕝᕕᒋᔭᐅᔪᑦ ↗