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Binomial and Geometric Probability Models

Binomial and Geometric Probability Models
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2018-01-31 09:09
FunctionProbability & StatisticsGeometric Construction
This example demonstrates the graphical representation of binomial and geometric probability distributions, involving core concepts like probability statistics, expected value, random variables, and distribution curves. Construction highlights include GeoGebra commands/objects like p (probability parameter) and A2-A26 (variables and graphical elements). Suitable for high school students and math enthusiasts studying probability theory and visualization applications.

GeoGebra Commands & Parameters

  1. Numeric p(0.8)
  2. Numeric A2(0)
  3. Numeric n(10)
  4. Numeric A3(1)
  5. Numeric A4(2)
  6. (2 * A4) - A3
  7. (2 * A5) - A4
  8. ((n! / ((A3! * (n - A3)!)) * p^(A3)) * (1 - p)^(n - A3))
  9. ((n! / ((A4! * (n - A4)!)) * p^(A4)) * (1 - p)^(n - A4))
  10. ((n! / ((A5! * (n - A5)!)) * p^(A5)) * (1 - p)^(n - A5))
  11. ((n! / ((A6! * (n - A6)!)) * p^(A6)) * (1 - p)^(n - A6))
  12. (2 * A6) - A5
  13. ((n! / ((A7! * (n - A7)!)) * p^(A7)) * (1 - p)^(n - A7))
  14. ((n! / ((A2! * (n - A2)!)) * p^(A2)) * (1 - p)^(n - A2))
  15. (A2, B2)
  16. (A3, B3)
  17. (A4, B4)
  18. (A5, B5)
  19. (A6, B6)
  20. (A7, B7)
  21. {A, B, C, D, E, F}
  22. (2 * A7) - A6
  23. (2 * A8) - A7
  24. (2 * A9) - A8
  25. (2 * A10) - A9
  26. (2 * A11) - A10
  27. (2 * A12) - A11
  28. (2 * A13) - A12
  29. (2 * A14) - A13
  30. (2 * A15) - A14
  31. (2 * A16) - A15
  32. (2 * A17) - A16
  33. (2 * A18) - A17
  34. (2 * A19) - A18
  35. (2 * A20) - A19
  36. (2 * A21) - A20
  37. (2 * A22) - A21
  38. (2 * A23) - A22
  39. (2 * A24) - A23
  40. (2 * A25) - A24
  41. (2 * A26) - A25
  42. (2 * A27) - A26
  43. (2 * A28) - A27
  44. (2 * A29) - A28
  45. ((n! / ((A8! * (n - A8)!)) * p^(A8)) * (1 - p)^(n - A8))
  46. ((n! / ((A9! * (n - A9)!)) * p^(A9)) * (1 - p)^(n - A9))
  47. ((n! / ((A10! * (n - A10)!)) * p^(A10)) * (1 - p)^(n - A10))
  48. ((n! / ((A11! * (n - A11)!)) * p^(A11)) * (1 - p)^(n - A11))
  49. ((n! / ((A12! * (n - A12)!)) * p^(A12)) * (1 - p)^(n - A12))
  50. ((n! / ((A13! * (n - A13)!)) * p^(A13)) * (1 - p)^(n - A13))
  51. ((n! / ((A14! * (n - A14)!)) * p^(A14)) * (1 - p)^(n - A14))
  52. ((n! / ((A15! * (n - A15)!)) * p^(A15)) * (1 - p)^(n - A15))
  53. ((n! / ((A16! * (n - A16)!)) * p^(A16)) * (1 - p)^(n - A16))
  54. ((n! / ((A17! * (n - A17)!)) * p^(A17)) * (1 - p)^(n - A17))
  55. ((n! / ((A18! * (n - A18)!)) * p^(A18)) * (1 - p)^(n - A18))
  56. ((n! / ((A19! * (n - A19)!)) * p^(A19)) * (1 - p)^(n - A19))
  57. ((n! / ((A20! * (n - A20)!)) * p^(A20)) * (1 - p)^(n - A20))
  58. ((n! / ((A21! * (n - A21)!)) * p^(A21)) * (1 - p)^(n - A21))
  59. ((n! / ((A22! * (n - A22)!)) * p^(A22)) * (1 - p)^(n - A22))
  60. ((n! / ((A23! * (n - A23)!)) * p^(A23)) * (1 - p)^(n - A23))