Statistical inference formulasheet

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Statistical inference formulasheet

  1. 1. Statistical Inference1. P(X = x) = nCx px(1 – p)n – x2. P(X=x) = e λ−!xxλ3. P(X = x) = !x!...x!xN!n2111xP x 22xP x 33xP . . . . xnnP4. λ = np 5. Z =σµ−x6. P = 7. Z =nx/σµ−8. t =nsx/µ−9. σ2= -10. s = ( )1/22−Σ−Σnnxx11. S.E(x) =12. Var(x) = – 13. μ =14. x = 15. x ± Zα/216. x ± t 2αnS17. W1- α = - Wα18. M1-α = n1(n1 + n2 +1) – Mα 19. E = Zα/220. Z =)2/()/()()(221212121nnxxσσµµ+−−−21. t =21212111)()(nnSpxx+−−− µµ22. Sp =2)1()1(21222211−+−+−nnSnSn23. t =2221212121 )()(nSnSxx+−−− µµ24.11 22222121212222121−+−+=∆nnSnnSnSnS25. ( )21 xx − + Z 2α222121nnσσ+26. ( )21 xx − + t 2α222121nSnS+ 27. p + Z 2xnpp )1( −28. t =nsdd/29. Sd =1/)( 22−Σ−Σnndd30. d = 31. d.f = n – 132. d.f = n1 + n2 – 2 33. d.f = (r – 1) (c – 1)
  2. 2. 34. Z =npppp)1( −−35. Z =)11)(1()()(212121nnPPPPPPPP +−−−−36. PP =2121nnxx++37. X2= 21σ−nx s238. F = 2221SS39. (p1–p2)+Z 2α22211 )1()1(nppnpp −+−40. X2= }/){( 2EEo −Σ 41. E =42. d.f = (k - 1, n - k) 43. RP = 2wSxwxxΣΣ44. Sxx = nxx /)( 22Σ−Σ 45. Sxy = nyxyx /))(( ΣΣ−Σ46. Syy = nyy /)( 22Σ−Σ 47. b1 =SxxSxy48. b0 = y - b1 1x 49. r = Sxy / yyxx SS50. t =SxxSeb/151. Se =2−nSSE52. t =21 2−−nrr53. β1 ± t 2αSxxSe54. SST = nxx /)( 22Σ−Σ 55. SSE = SST – SSTR56. SSTR = ∑ – 57. r12 = 222221212121)()( xxnxxnxxxxnΣ−ΣΣ−ΣΣΣ−Σ58. MSE = 59. MSTR =60. F-Ratio = 61. R1.23 = 22313231221321212rrrrrr−−+62. r12 = 63. SSR =64. SST = Syy 65. d.f = (n1 – 1) , (n2 – 1)66.( )( )2232132313123.1211 rrrrrr−−−= 67. F =68. SSR = b0Σy + b1 Σx1y + b2 Σx2y -69. rs = 1 -70. H = ×Σ - 3(n + 1) 71. X ± A2 R
  3. 3. 72. C ± 3 Sc 73. Sc =74. P ± 3 75. UCLR = D4 R76. LCLR = D3 R 77. P(X=x) = n-1Cx-1 × px× (1 – p)n-x78. P = 79. σ =

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