[PyConKR2017] 온라인 게임에서의 이항 분포

Transcript

1. ৡۄੋ ѱ੐ীࢲ੄ ੉೦࠙ನ ই੉మ ъച ഛܫ ࠙ࢳ -[|]- Box and

   Whisker ߅੢द

2. Ѿҗܳ ঌ ࣻ হח प೷

3. ಴ࠄ ҕр ز੹ ؍૑ӝ H T Prob: 0.5 Prob: 0.5

4. ಴ࠄ ҕр ই੉మ ъച S F Prob: 0.1 Prob: 0.9

5. ഛܫ ߸ࣻ X S F Prob: 0.1 Prob: 0.9 0

   1 2 3 4 5 X

6. ഛܫ ߸ࣻ X = x X = x {s ∈

   S : X(s) = x} X = 1 {success} X = 0 {fail} S F Prob: 0.1 Prob: 0.9 0 1 2 3 4 5 X

7. ഛܫ ೣࣻ P(X=x) = f(x) P(X = x) = f(x)

   P(X = 1) = f(1) = 0.1 P(X = 0) = f(0) = 0.9 S F Prob: 0.1 Prob: 0.9 0 1 2 3 4 5 X f 0 1 0.1 0.9 x p

8. ߬ܰ־੉ द೯ https://en.wikipedia.org/wiki/Bernoulli_trial S F Prob: 0.1 Prob: 0.9 0

   1 2 3 4 5 X f 0 1 0.1 0.9 x p

9. ੉೦ ࠙ನ https://en.wikipedia.org/wiki/Binomial_distribution

10. ੉೦ ࠙ನ https://en.wikipedia.org/wiki/Binomial_distribution 0 0 1 2 3 4 5

    X f 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10

11. ੉೦ ࢎѤ੄ ࣻ 1 2 3 4 5

12. ੉೦ ࠙ನ vs ਺੉೦ ࠙ನ ੉೦࠙ನ fixed n: ୨ द೯

    ࣻ p: ࢿҕ ഛܫ variable k: ࢿҕ പࣻ k <= n count ੿೧૓ द೯ പࣻ ೞীࢲ ࢿҕೞח പࣻ ਺੉೦࠙ನ fixed n: ୨ ࢿҕ പࣻ p: ࢿҕ ഛܫ variable k: पಁ പࣻ 0 <= k < inf count ੿೧૓ ࢿҕ പࣻܳ ׳ࢿೡ ٸө૑ पಁೞח പࣻ

13. ਺੉೦ ࠙ನ https://en.wikipedia.org/wiki/Negative_binomial_distribution

14. ਺੉೦ ࠙ನ https://en.wikipedia.org/wiki/Negative_binomial_distribution 0 0 1 2 3 4 5

    X f 1 2 3 4 5 6 7 8 9 inf 6 7 8 inf

15. ਺੉೦ ࢎѤ੄ ࣻ 1 2 3 4 p

16. ਺੉೦ ࠙ನ੄ ׮ܲ ಴ӝߨ k: पಁ, n: ࢿҕ k: ࢿҕ,

    r: पಁ nCr = nCn-r 5 choose 3 = 5 choose 2 x: ୨ दب, r: पಁ x = k + r

17. P(X<=90) = ?

18. P(X<=?) = 0.5

19. P(X<=?) = 0.99

20. P(X<=?) = 1.0

21. ؊ ࠂ੟ೠ ޙઁ: ݽ੄प೷

22. None

23. جܿ౸ 0 0.1

24. +6ъ 100,000 ݺ

25. +7ъ 100,000ݺ

26. +10ъ 100,000ݺ

27. Q & A