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Definite Integral and Poisson Distribution

Definite Integral and Poisson Distribution
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2018-03-20 09:51
FunctionIntegralProbability & Statistics
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This example illustrates the relationship between definite integrals and the Poisson distribution. It uses dynamic coordinates and vectors to demonstrate how to calculate the integral of a probability distribution function. Commands like Point, Vector, Sequence, and DynamicCoordinates are employed. Suitable for high school mathematics, particularly calculus and probability statistics courses.

GeoGebra Commands & Parameters

  1. Point(Sequence[A + (i, 0), i, 1, 20, 1]) → B
  2. Vector(A, C1) → u
  3. Sequence(A + (i * UnitVector[Segment[A, C1]]), i, 1, 20, 1) → UPoints
  4. DynamicCoordinates(C1, x(ClosestPoint[UPoints, C1]), y(ClosestPoint[UPoints, C1])) → C
  5. Vector(B, C2) → v
  6. Sequence((x(B) + (Length[v] * cos(t°)), y(B) + (Length[v] * sin(t°))), t, 0, 355, 5) → VPoints
  7. DynamicCoordinates(C2, x(ClosestPoint[VPoints, C2]), y(ClosestPoint[VPoints, C2])) → C'
  8. Segment(A, C) → f
  9. Intersect(Circle[A, f], Line[B, C']) → G, G'
  10. Segment(A, B) → g
  11. Segment(C', B) → h
  12. Polygon(A, B, G) → t1, g_1, a, b
  13. Polygon(A, B, G') → t2, i, j, k
  14. If(C ≟ G ∧ C' ≟ G, true, false) → closed1
  15. If(C ≟ G' ∧ C' ≟ G', true, false) → closed2
  16. Angle(C', B, A) → α
  17. Intersect(Circle[D, 5], Ray[E, Rotate[D, (-(45°)), E]], 2) → F
  18. Polygon(D, E, F) → t3, f_1, d_1, e
  19. Angle(F, E, D) → β

AI Drawing Prompt Reference

Draw a dynamic illustration showing the relationship between definite integrals and the Poisson distribution, featuring a sequence of points and vectors, calculated using dynamic coordinates and vectors to demonstrate the integral of a probability distribution function, starting with point sequences and vectors, then determining key points with dynamic coordinates, and finally drawing polygons and intersecting circles to represent integral regions and distribution shapes.
The prompt above was compiled from the original drawing commands and is for reference only.