Takayuki Uchiba
November 15, 2020
420

# statistician_ja_lt5.pdf

## Takayuki Uchiba

November 15, 2020

## Transcript

2. ### Ұ༷࠷খ෼ࢄෆภਪఆྔ  ͷҰ༷࠷খ෼ࢄෆภਪఆྔʢ6.76&ʣɹ  ෆภੑ ͕ͲΜͳ஋Ͱ͋ͬͯ΋ɺ ͕੒Γཱͭɻ  Ұ༷࠷খ෼ࢄੑ ͕ͲΜͳ஋Ͱ͋ͬͯ΋ɺଞͷෆภਪఆྔ

ʹൺ΂ͯ ͷ෼ࢄ͕খ͍͞ɻཁ͢Δʹɺ ͕੒Γཱͭɻ ྫαΠζ ͷಠཱඪຊΛظ଴஋ ෼ࢄ ͷਖ਼ن෼෍͔Βಘͨ৔߹ ɾظ଴஋ ͷ6.76&ඪຊฏۉ ɾ෼ࢄ ͷ6.76&ෆภ෼ࢄ T θ θ [T] = θ θ S T [T] ≤ [S] n μ σ2 μ σ2

θ θ
6. ### ۩ମྫͷߏ੒ ֬཰ม਺ ͕࣍ͷ֬཰࣭ྔؔ਺  ʹै͍ͬͯΔ΋ͷͱ͠·͢ɻύϥϝʔλ ͷҰ༷࠷খ෼ࢄෆภਪఆྔ͸ଘࡏ͢Δ͔ʁ ٕज़తͳ3FNBSL Ͱද͞ΕΔͲΜͳ౷ܭྔ΋ɺ ͷܗͰද͢͜ͱ͕Ͱ͖Δɻ X

f(x) = { p JGx = − 1 (1 − p)2px JGx = 0,1,2,⋯ p X T(X) = ∞ ∑ x=−1 tx [X = x]
7. ### ෆภਪఆྔʹͳΔͨΊͷ৚݅ Λ༻͍ͯɺ౷ܭྔ ͷظ଴஋Λܭࢉ͢Δɻ  ౷ܭྔ ͕ෆภਪఆྔͳΒ͹ɺظ଴஋͸ඞͣ ʹ౳͘͠ͳΔɻ ˠɹ઴Խࣜ GPS 

  ˠɹ ͷܗͰද͞ΕΔ౷ܭྔ ͕ෆภਪఆྔʹͳΔɻ f(x) = { p JGx = − 1 (1 − p)2px JGx = 0,1,2,⋯ T(X) [T] = t−1 p + ∞ ∑ x=0 tx (1 − p)2px = t0 + ∞ ∑ x=1 (tx−2 − 2tx−1 + tx )px T(X) p tx − 2tx−1 + tx−2 = 0 x ≥ 2 t1 = 1 − t−1 t0 = 0 tx = x(1 − t−1 ) T(X)
8. ### ෆภਪఆྔͷ෼ࢄΛܭࢉ͢Δʢͦͷʣ Λ༻͍ͯɺෆภਪఆྔ ͷ෼ࢄΛܭࢉ͢Δɻ ͜͏͍͏ͱ͖ʹ໾ཱͭͷ͸෼ࢄͷެࣜʂ  ͳͷͰɺ Λܭࢉ͠Α͏ɻ f(x) = {

p JGx = − 1 (1 − p)2px JGx = 0,1,2,⋯ T(X) [T] = [T2] − [T]2 = [T2] − p2, ෆภੑ [T2]
9. ### ෆภਪఆྔͷ෼ࢄΛܭࢉ͢Δʢͦͷʣ  Ώ͑ʹɺ ͷ෼ࢄ͸ ͱΘ͔Γ·͢ɻ [T2] = t2 −1 p

+ ∞ ∑ x=1 x2(1 − t−1 )2(1 − p)2px = t−1 + (1 − t−1 )2(1 − p)2 ∞ ∑ x=1 x2px = t2 −1 p + (1 − t−1 )2(1 − p)2 p(1 + p) (1 − p)3 = t2 −1 p + (1 − t−1 )2 p(1 + p) 1 − p T(X) [T] = t2 −1 p + (1 − t−1 )2 p(1 + p) 1 − p − p2
10. ### ෼ࢄ͕࠷খ஋ΛͱΔͨΊͷ৚݅ʢͦͷʣ ࠷খ෼ࢄΛ༩͑Δ ʢΛ༩͑Δ ʣΛٻΊɺ ʹґଘͳΒ6.76&͸ଘࡏ͠ͳ͍ɻ Λ Ͱ੔ཧ͢Δͱɺ࣍ؔ਺͕ݱΕΔɻ  ฏํ׬੒ͯ͠ɺ࠷খ஋Λ༩͑Δ ΛٻΊͯΈΑ͏ʂ

T(X) t−1 p [T] = t2 −1 p + (1 − t−1 )2 p(1 + p) 1 − p − p2 t−1 [T] = (p + p(1 + p) 1 − p ) t2 −1 − 2 p(1 + p) 1 − p t−1 + ( p(1 + p) 1 − p − p2 ) t−1
11. ### ෼ࢄ͕࠷খ஋ΛͱΔͨΊͷ৚݅ʢͦͷʣ ฏํ׬੒͢Δͱɺ࣍ͷΑ͏ʹͳΓ·͢ɻ  ࣍ؔ਺ͷ௖఺ͷ࠲ඪΛಡΉ͜ͱͰɺ ͷͱ͖෼ࢄ࠷খͱΘ͔Γ·͢ɻ [T] = (p + p(1

+ p) 1 − p ) t−1 − 1 1 + 1 − p 1 + p 2 + const . = (p + p(1 + p) 1 − p ) {t−1 − p + 1 2 } 2 + const . t−1 = p + 1 2
12. ### ݁࿦ ෼ࢄ͕࠷খʹͳΔෆภਪఆྔ͕ύϥϝʔλ ͷ஋ʹґଘ͍ͯ͠Δɻ ˠɹ ͷ6.76&͸ଘࡏ͠ͳ͍ʂʂʂʂʂ ͜ͷྫ͕ڭ͑ͯ͘Ε͍ͯΔͱࢥ͏͜ͱʢࢲײʣ ɾඞͣ͠΋ʮ͍ͭͰ΋҆ఆͯ͠ਫ਼౓͕ྑ͍ਪఆྔʯ͕ଘࡏ͢Δͱ͸ݶΒͳ͍ɻ ɾԾઆ͕͋ΔͳΒਪఆྔʹ൓өͤͯ͞ΈΔͷ΋େࣄɻ ɹɾࠓճͷྫͰ΋ɺ ͷ஋ʹԠͨ͡ਪఆྔͷબ୒ͷ༨஍͸࢒͞Ε͍ͯΔɻ

ɹɾDMJDL཰͸খ͘͞ͳΓ͕͔ͪͩΒɺͪΐͬͱॖখͨ͠΋ͷΛ࢖͓͏ͱ͔ɻ p p p
13. ### ͝ਗ਼ௌ͋Γ͕ͱ͏͍͟͝·ͨ͠ʂ ࣗݾ঺հͰ΋΍ͬͱ͖·͢ɻɻɻ ɾ!VUBLB ɾגࣜձࣾ͢͏͕͘ͿΜ͔ ڭ຿෦ ෦௕ ɾڵຯ਺ཧ౷ܭֶͷσʔλϚΠχϯά΁ͷԠ༻ ୅਺زԿֶ ɾ࿦จ ɹओஶ(MVJOH4UBCJMJUZ\$POEJUJPOTPO3VMFE4VSGBDFXJUI1PTJUJWF(FOVT

 ɹɹɹɹ0TBLB+PVSOBMPG.BUIFNBUJDT BDDFQUFE   ɹڞஶࠓ೥͸ຊɺ͍ͣΕ΋ػցֶशͷ࿦จɻ