Loi binomiale
Author: Johann DOLIVET
Date: 13 Avril 2013

Représentation graphique de la loi binomiale selon les valeurs des paramètres n (nombre d'épreuves) et p (probabilité de succès de l'épreuve de Bernoulli).
Vous pouvez recadrer la fenêtre lorsque vous modifiez le paramètre n (Clic Droit).

n+1

1

0

Loi binomiale de paramètres n et p

Loi \;  binomiale \;  de \;  paramètre \;  n \;  et \;  p

n = 17 (slider from 1 to 100, step 1)
p = 0.56 (slider from 0 to 1, step 0.01)
A = (-1, -0.1)
B = (-1, 1.2)
C: (n + 1, 0)
D = (0, 1)
E = (0, 0)
liste1 = Sequence((i, ((Binomial[n, i] * (1 - p)^(n - i)) * p^(i))), i, 0, n)
liste3 = Sequence(Segment[(i / n, 0), (i / n, ((Binomial[n, i] * (1 - p)^(n - i)) * p^(i)))], i, 0, n)
a: x = p
F = Intersect(b, a)
G = Intersect(xAxis, a)
c = Segment(F, G)
d: x = sqrt(((n * p) * (1 - p))) / n + p
e: x = p - sqrt(((n * p) * (1 - p))) / n
H = Intersect(b, d)
I = Intersect(e, b)
J = Intersect(xAxis, e)
K = Intersect(d, xAxis)
poly1, i, h, k_1, j = Polygon(I, H, K, J)
L = (1, 0)
texte2: "" + n + ""
k = 7 (slider from 0 to n, step 1)
M: (k / n, ((Binomial[n, k] * p^(k)) * (1 - p)^(n - k)))
N: (0, ((Binomial[n, k] * p^(k)) * (1 - p)^(n - k)))
texte6: "" + (((Binomial[n, k] * p^(k)) * (1 - p)^(n - k))) + ""
O: (k / n, 0)
texte7: "" + k + ""
texte8: "μ=" + (LaTeX[(n * p)]) + ""
P = Intersect(a, f)
Q = Intersect(d, f)
u = Vector(P, Q)
v = Vector(Q, P)
R = Midpoint(P, Q)
texte9: "σ=" + (LaTeX[sqrt(((n * p) * (1 - p)))]) + ""
texte5: "p(X=" + (LaTeX[k]) + ")=\binom{" + (LaTeX[n]) + "}{" + (LaTeX[k]) + "}" + (LaTeX[p]) + "^" + (LaTeX[k]) + "×" + (LaTeX[1 - p]) + "^{" + (LaTeX[n - k]) + "}=" + (LaTeX[((Binomial[n, k] * p^(k)) * (1 - p)^(n - k))]) + ""
texte4: "X\sim{B}(" + (LaTeX[n]) + ";" + (LaTeX[p]) + ")"

Tool: ArcEllipse
Input: A, B, C, ellipse
Output: arc

O = Center(ellipse)
arc1 = Arc(ellipse, A, C)
arc2 = Arc(ellipse, C, A)
α = Angle(Vector[O, A], Vector[O, C])
β = Angle(Vector[O, A], Vector[O, B])
arc = If(β > α, arc2, arc1)

Tool: Cadre
Input: A, B
Output: poly1

a = OrthogonalLine(A, xAxis)
b = OrthogonalLine(B, xAxis)
c = OrthogonalLine(A, yAxis)
d = OrthogonalLine(B, yAxis)
C = Intersect(a, d)
D = Intersect(b, c)
poly1, c_1, b_1, d_1, a_1 = Polygon(C, B, D, A)

Tool: f_{Box}
function f, lower left point of box, upper right point of box
Input: f, A, B
Output: fbox

f(x) = (4 * sin(x))
fbox(x) = If[x(A) ≤ x ≤ x(B), ((f(x) + y(A)) / 2 + abs(f(x) - y(A)) / 2 + y(B)) / 2 - abs((f(x) + y(A)) / 2 + abs(f(x) - y(A)) / 2 - y(B)) / 2,NaN]

Tool: Coordonnées
Permet d'obtenir les pointillés pour les coordonnées
Input: C
Output: e, f

c = OrthogonalLine(C, xAxis)
d = OrthogonalLine(C, yAxis)
D = Intersect(xAxis, c)
E = Intersect(d, yAxis)
e = Segment(D, C)
f = Segment(C, E)