LABORATORITRAIM 06df = 36α = 0.05sid 99

Bias bilong Wil bilong Rulet

Wil bilong rulet i gat bias i laikim sampela hul long wanem samting i bagarap: liklik banis i lus, rota i no stret, ol hul i bagarap. Bias bilong wil bilong rulet i stap tru na sampela man i bin kisim win long en. Hevi em olsem stretpela wil tru i save kamapim “hat namba” oltaim, olsem na askim i no olsem wanpela namba i hat o nogat, tasol olsem olgeta pasin i no stret moa long sans inap kamapim.

1. Kisim eksampel long stretpela wil

Ol tanim i kam long wil long simulesen i nogat bias liklik. Senisim hamas samting yu kaunim na lukim hul i hat tru.

0321519421225173462713361130823105241633120143192218297281235326
tanim370
ol i ting long wanwan hul10.0
hul i hat tru20 · 16 taim (4.32%)
hul i hat tru na namba ol i ting+60% · 1.9σ
chi-square · p32.8 · 0.622
tok pinisnogat mak bilong bias

2. Wanem i kamap na wanem ol i ting

Wanwan ba em i wanpela hul long lain bilong wil. Lain i bruk em namba ol i ting, n/37. Hap i gat kala em ±2 standet diviesen: long stretpela wil klostu wanpela hul long twenti bai go ausait long en long sans tasol.

0ol hul long lain bilong wil →26

3. Chi-square tes

Tes i bungim hamas longwe olgeta hul i stap long namba ol i ting, taim em yet na skelim. Long stretpela wil, namba i bung i bihainim chi-square distribution wantaim 36 degri bilong fridom; p-velyu i daunbilo long 0.05 ol i save kolim olsem i makim samting.

χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ Eᵢ = n/37 df = 36
n = 370 · E = 10.00 · χ² = 32.80 · p = 0.622
Tok lukaut long hamas samting yu kaunimDaunbilo long klostu 1,000 tanim, tes i no gat strong long painim ol bias i ken kamap tru, na risal “i makim samting” long p < 0.05 bai kamap long sans long 1 long olgeta 20 eksampel bilong stretpela wil yu lukim. Sapos yu testim planti wil, o testim wankain wil gen na gen inap em i pas, yu bai kisim giaman mak tru.

4. Hamas tanim yu bai nidim

Hamas tanim yu nidim long painimaut wanpela hul i kamap planti moa long 1/37, long mak 5% long wanpela sait wantaim strong 80%. Hul i kamap 1 taim long 35, i no 1 long 37, bai givim strongpela edj long pleia, na yu nidim planti ten tausen tanim yu raitim long soim em i tru.

namba truedj bilong pleiatanim yu nidimlong 40 tanim/h
1 long 25+44.0%1,10828 h
1 long 30+20.0%4,392110 h
1 long 33+9.1%15,747394 h
1 long 35+2.9%69,4611,737 h
Long soim bias tru, yu mas raitim ol tanim long olgeta nait, planti ten tausen.

Metodoloji

Kisim eksampel. Ol namba i kam wankain long 37 hul long jenereta i gat sid (mulberry32, sid 99), olsem na pes i save kamapim wankain risal gen.
Tes. Pearson chi-square tes bilong skelim, 36 degri bilong fridom, p-velyu i kam long regularized incomplete gamma function.
Strong bilong tes. Normal approximation long one-proportion tes, α = 0.05 long wanpela sait, strong 0.80.
Hap bilong en. Painimaut long statistik tasol. Ol as bilong bodi na skelim long seksen (i no long wanwan hul) i stap long Skelim Ol Seksen.

Liklik lap

Stretpela wil i save kamapim hat namba long olgeta nait. Long soim bias tru, yu nidim planti ten tausen tanim.

Stretpela wil i save kamapim hat namba long olgeta nait. Long soim bias tru, yu nidim planti ten tausen tanim.

Ol As bilong Save

  1. Pearson, K. (1900). On the criterion that a given system of deviations… Philosophical Magazine, 50(302).
  2. Thorp, E. O. (1969). Optimal gambling systems for favorable games. Review of the International Statistical Institute, 37(3).
  3. Ethier, S. N. (2010). The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer. Ch. 13, Roulette.