ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤ
ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱨᱩᱞᱮᱴ ᱥᱴᱨᱮᱴᱮᱡᱤ ᱫᱚ ᱡᱚᱛᱚ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱨ ᱜᱩᱱ ᱮᱫᱟ ᱟᱨ ᱡᱤᱛ ᱛᱟᱭᱚᱢ ᱵᱮᱥ ᱵᱟᱡᱤ ᱛᱮ ᱨᱩᱣᱟᱹᱲᱚᱜ-ᱟ᱾ ᱡᱚᱛᱚ ᱡᱤᱛ ᱫᱚ ᱞᱟᱦᱟ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱦᱟᱹᱱᱤ ᱟᱨ ᱢᱤᱫ ᱵᱮᱥ ᱭᱩᱱᱤᱴ ᱨᱩᱣᱟᱹᱲ ᱟᱹᱜᱩ ᱮᱫᱟ᱾ ᱞᱟᱛᱟᱨ ᱨᱮᱭᱟᱜ ᱥᱟᱦᱴᱟ ᱫᱚ ᱩᱫᱩᱜ ᱮᱫᱟ ᱡᱮ ᱱᱚᱣᱟ ᱫᱚ ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱨᱮ ᱪᱮᱫ ᱮ ᱠᱚᱨᱟᱣᱟ, ᱟᱨ ᱪᱮᱫᱟᱜ ᱱᱚᱣᱟ ᱫᱚ ᱟᱸᱫᱟᱡᱽ ᱦᱟᱹᱱᱤ ᱵᱟᱝ ᱵᱚᱫᱚᱞ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱨᱩᱞᱮᱴ ᱥᱤᱥᱴᱮᱢ ᱪᱮᱫ ᱞᱮᱠᱟ ᱪᱟᱞᱟᱜ-ᱟ?
ᱦᱟᱨᱟᱣ ᱠᱷᱟᱱ ᱵᱟᱨ ᱜᱩᱱ᱾ ᱡᱤᱛᱟᱹᱣ ᱠᱷᱟᱱ ᱵᱮᱥ ᱵᱟᱡᱤ ᱛᱮ ᱨᱩᱣᱟᱹᱲ᱾ ᱚᱱᱟ ᱜᱮ ᱡᱚᱛᱚ ᱥᱤᱥᱴᱮᱢ ᱠᱟᱱᱟ᱾ $10 ᱵᱮᱥ ᱵᱟᱡᱤ ᱟᱨ $500 ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹ ᱥᱟᱶ ᱛᱟᱹᱞᱤᱠᱟᱹ ᱫᱚ ᱛᱩᱨᱩᱭ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱢᱩᱪᱟᱹᱫᱚᱜ-ᱟ᱾ ᱢᱩᱪᱟᱹᱫ ᱠᱚᱞᱚᱢ ᱫᱚ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮ ᱚᱱᱟ ᱫᱷᱟᱯ ᱦᱟᱹᱵᱤᱡ ᱥᱮᱴᱮᱨ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱠᱟᱱᱟ, ᱡᱟᱦᱟᱸ ᱨᱮ ᱡᱚᱛᱚ ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ 19/37 ᱠᱟᱱᱟ᱾
ᱵᱮᱥ ᱵᱟᱡᱤ $10, ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹ $500᱾ ᱛᱩᱨᱩᱭ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱫᱟᱨᱟᱭ ᱵᱟᱡᱤ ᱫᱚ $640 ᱠᱟᱱᱟ, ᱥᱤᱢᱟᱹ ᱠᱷᱚᱱ ᱵᱮᱥᱤ: ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱫᱚ $630 ᱦᱟᱹᱱᱤ ᱥᱟᱶ ᱨᱟᱹᱯᱩᱫᱚᱜ-ᱟ᱾ ᱟᱨᱟᱜ ᱨᱮ ᱞᱟᱜᱟᱛᱟᱨ ᱛᱩᱨᱩᱭ ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ (19/37)^6 = 1.83% ᱠᱟᱱᱟ, ᱥᱟᱦᱟ ᱡᱚᱛᱚ 55 ᱪᱮᱥᱴᱟ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ᱾
ᱥᱤᱥᱴᱮᱢ ᱛᱮ ᱥᱮᱱ ᱯᱮ
ᱦᱟᱹᱱᱤ ᱫᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱟᱨ ᱫᱷᱟᱣ ᱮᱫᱟ᱾ ᱡᱤᱛ ᱫᱚ ᱮᱦᱚᱵ ᱛᱮ ᱨᱩᱣᱟᱹᱲ ᱮᱫᱟ᱾
ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱟᱨ ᱨᱮᱡᱟᱞᱴ ᱫᱚ ᱢᱩᱞ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱭᱩᱱᱤᱴ ᱨᱮ ᱢᱮᱱᱟᱜ-ᱟ᱾
ᱢᱤᱫ ᱥᱮᱥᱚᱱ ᱪᱮᱫ ᱞᱮᱠᱟ ᱧᱮᱞᱚᱜ-ᱟ?
ᱦᱩᱰᱤᱧ ᱦᱩᱰᱤᱧ ᱫᱷᱟᱯ ᱪᱮᱛᱟᱱ ᱛᱮ, ᱛᱟᱭᱚᱢ ᱛᱮ ᱢᱤᱫ ᱜᱟᱰᱟ᱾ ᱨᱩᱞᱮᱴ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ ᱨᱮ ᱵᱟᱨ ᱜᱩᱱ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱯᱩᱨᱟᱹᱣ ᱞᱟᱜᱟᱛᱟᱨ ᱫᱚ ᱢᱤᱫ ᱵᱮᱥ ᱵᱟᱡᱤ ᱥᱮᱞᱮᱫ ᱮᱫᱟ, ᱚᱱᱟᱛᱮ ᱫᱟᱜ ᱫᱚ ᱞᱟᱜᱟᱛᱟᱨ ᱪᱮᱛᱟᱱ ᱛᱮ ᱟᱨᱚᱜ-ᱟ᱾ ᱡᱟᱦᱟᱸ ᱞᱟᱜᱟᱛᱟᱨ ᱫᱚ $500 ᱥᱤᱢᱟᱹ ᱨᱮ ᱛᱟᱹᱠᱩᱢᱚᱜ-ᱟ ᱚᱱᱟ ᱫᱚ ᱢᱤᱫ ᱫᱷᱟᱣ ᱛᱮ $630 ᱨᱩᱣᱟᱹᱲ ᱤᱫᱤ ᱮᱫᱟ: ᱚᱱᱟ ᱫᱷᱟᱯ ᱠᱚ ᱠᱷᱚᱱ 63᱾
- p10 −$1,000
- p25 −$1,000
- ᱢᱤᱰᱤᱭᱟᱱ −$1,000
- p75 +$930
- p90 +$1,830
ᱥᱤᱢᱩᱞᱮᱴᱚᱨ
ᱡᱚᱛᱚ ᱥᱮᱴᱤᱝ ᱫᱚ $1,000 ᱠᱷᱮᱞ ᱯᱩᱸᱡᱤ ᱠᱷᱚᱱ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ 2,000 ᱥᱮᱥᱚᱱ ᱪᱟᱞᱟᱣ ᱮᱫᱟ᱾ ᱨᱮᱡᱟᱞᱴ ᱫᱚ ᱛᱩᱨᱟᱹᱫ ᱵᱚᱫᱚᱞᱚᱜ-ᱟ᱾
ᱟᱹᱰᱤ ᱵᱮᱥᱤ ᱥᱮᱥᱚᱱ ᱫᱚ ᱦᱩᱰᱤᱧ ᱞᱟᱵᱷ ᱨᱮ ᱢᱩᱪᱟᱹᱫᱚᱜ-ᱟ (40.8%), ᱚᱱᱟ ᱜᱮ ᱫᱚ ᱟᱠᱚᱨᱥᱚᱬ ᱠᱟᱱᱟ᱾ ᱟᱣᱥᱚᱛ ᱫᱚ ᱢᱟᱭᱤᱱᱟᱥ (−$66.44), ᱪᱮᱫᱟᱜ ᱥᱮ ᱦᱟᱹᱱᱤ ᱥᱮᱥᱚᱱ ᱠᱚ ᱢᱟᱨᱟᱝ: 59.3% ᱥᱮᱥᱚᱱ ᱨᱮ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱫᱚ ᱴᱮᱵᱩᱞ ᱥᱤᱢᱟᱹ ᱛᱮ ᱥᱮᱴᱮᱨ ᱮᱱᱟ᱾ ᱚᱱᱟ ᱜᱮ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱞᱮᱠᱟᱱ $10 ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱤᱭᱟᱹ ᱫᱚ ᱢᱚᱴᱟ ᱢᱩᱴᱤ $27 ᱦᱟᱨᱟᱣ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱢᱮᱱᱟᱜ-ᱟ᱾
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 ᱵᱟᱡᱤ ᱵᱟᱨ ᱫᱷᱟᱣ ᱠᱟᱫ ᱢᱤᱫ ᱢᱟᱨᱴᱤᱝᱜᱮᱞ 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 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
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᱾
ᱜᱮᱞᱢᱚᱬᱮ ᱦᱟᱹᱱᱤ ᱨᱮᱭᱟᱜ ᱞᱟᱜᱟᱛᱟᱨ ᱫᱚ ᱥᱟᱦᱟ 22,000 ᱪᱮᱥᱴᱟ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱚᱱᱟ ᱫᱚ ᱵᱮᱥ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ᱾ ᱢᱮᱱᱠᱷᱟᱱ ᱵᱟᱨ ᱠᱟᱨᱚᱬ ᱛᱮ ᱵᱟᱝ᱾ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱫᱚ ᱢᱤᱫ ᱱᱟᱣᱟ ᱪᱮᱥᱴᱟ ᱮᱦᱚᱵ ᱮᱫᱟ, ᱟᱨ ᱢᱤᱫ ᱟᱭᱩᱵ ᱨᱮ ᱥᱟᱭ ᱥᱟᱭ ᱜᱷᱩᱨᱟᱹᱣ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱟᱨ ᱡᱟᱦᱟᱱ ᱦᱚᱸ ᱜᱮᱞᱢᱚᱬᱮ ᱦᱟᱹᱵᱤᱡ ᱵᱟᱝ ᱥᱮᱴᱮᱨᱚᱜ-ᱟ: $10 ᱵᱮᱥ ᱠᱷᱚᱱ $500 ᱥᱤᱢᱟᱹ ᱫᱚ ᱛᱩᱨᱩᱭ ᱦᱟᱹᱱᱤ ᱛᱟᱭᱚᱢ ᱵᱟᱨ ᱜᱩᱱ ᱵᱚᱸᱫ ᱮᱫᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱟᱦᱟ 55 ᱪᱮᱥᱴᱟ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱩᱭᱩᱜ-ᱟ᱾
ᱱᱚᱣᱟ ᱫᱚ ᱪᱮᱫᱟᱜ ᱚᱰᱥ ᱵᱟᱝ ᱵᱚᱫᱚᱞ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ?
ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱫᱚ ᱡᱚᱲᱟᱣᱚᱜ-ᱟ᱾ ᱡᱩᱫᱤ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱸᱫᱟᱡᱽ ᱫᱚ ᱟᱡᱟᱜ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −2.70% ᱠᱟᱱᱟ, ᱛᱚᱵᱮ ᱡᱟᱦᱟᱱ ᱵᱟᱡᱤ ᱛᱟᱹᱞᱤᱠᱟᱹ ᱨᱮᱭᱟᱜ, ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱪᱮᱫ ᱞᱮᱠᱟ ᱦᱚᱸ ᱵᱟᱪᱷᱟᱣᱚᱜ ᱠᱟᱱ ᱛᱟᱦᱮᱸᱱ ᱠᱷᱟᱱ ᱦᱚᱸ, ᱟᱸᱫᱟᱡᱽ ᱫᱚ ᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱨᱮᱭᱟᱜ −2.70% ᱜᱮ ᱠᱟᱱᱟ᱾ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱵᱟᱪᱷᱟᱣ ᱫᱚ ᱞᱟᱦᱟ ᱨᱮᱡᱟᱞᱴ ᱨᱮ ᱟᱹᱛᱩᱠ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ; ᱫᱟᱨᱟᱭ ᱨᱮᱡᱟᱞᱴ ᱨᱮ ᱫᱚ ᱵᱟᱝ᱾
bᵢ ᱫᱚ i ᱜᱷᱩᱨᱟᱹᱣ ᱢᱟᱲᱟᱝ ᱨᱮ ᱵᱟᱪᱷᱟᱣᱚᱜ-ᱟ; Xᵢ = ±1 ᱫᱚ bᵢ ᱠᱷᱚᱱ ᱟᱡᱟᱫ
ᱡᱟᱹᱥᱛᱤ ᱪᱟᱞᱟᱜ ᱵᱷᱩᱞ ᱵᱩᱡᱷᱟᱹᱣ
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱟᱭᱢᱟ ᱦᱩᱰᱤᱧ ᱡᱤᱛ, ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱤᱡᱩᱜ ᱢᱟᱨᱟᱝ ᱦᱟᱹᱱᱤ᱾ ᱟᱨ ᱵᱤᱢᱟ ᱫᱟᱵᱤ ᱫᱚ ᱟᱯᱮ ᱟᱡ ᱛᱮ ᱜᱮ ᱯᱮ ᱵᱷᱩᱜᱛᱟᱱᱟ᱾
