prob-006-campana-gauss

Z

Intervalo

x_1

x_2

x_2 = -4.1 (slider from -4.1 to x_1, step 0.01)
x_1 = 1.31 (slider from -4.1 to 4.1, step 0.01)
σ = 0.5 (slider from 0 to 5, step 0.01)
μ = 0.8 (slider from -5 to 5, step 0.01)
f(x) = (1 / ((σ * sqrt((2 * π)))) * ℯ^(((-(x - μ)^(2))) / ((2 * σ^(2)))))
g(x) = (1 / sqrt((2 * π)) * ℯ^(((-x^(2))) / 2))
textog: "F(x)=P(Z\le x)=\int_\infty^x \dfrac{1}{σ \sqrt{2π}} e^{\dfrac{-(x - μ)²}{2σ²}} dx=\int_\infty^x " + (LaTeX[g]) + "dx"
textof: "F(x)=P(X\le x)=\int_\infty^x \dfrac{1}{σ \sqrt{2π}} e^{\dfrac{-(x - μ)²}{2σ²}} dx=\int_\infty^x " + (LaTeX[f]) + "dx"
area = Integral(f, x_2, x_1)
textoX: "X\equiv N(μ,σ)=N(" + (LaTeX[μ]) + "," + (LaTeX[σ]) + ")"
textoZ: "Z \equiv N(μ,σ)=N(" + (LaTeX[μ]) + "," + (LaTeX[σ]) + ")"
textoXZ = If(μ ≟ 0 ∧ σ ≟ 1, textoZ, textoX)
textofg = If(μ ≟ 0 ∧ σ ≟ 1, textog, textof)
a = false
textointZ: "P(x_2<Z<x_1)=
P(" + (LaTeX[x_2]) + "<Z<" + (LaTeX[x_1]) + ")=  " + (LaTeX[area]) + ""
textointX: "P(x_2<X<x_1)=
P( " + (LaTeX[x_2]) + "<X< " + (LaTeX[x_1]) + ")= " + (LaTeX[area]) + ""
textoint = If(μ ≟ 0 ∧ σ ≟ 1, textointZ, textointX)
textonointX: "P(X<x_1)=
P(X<  " + (LaTeX[x_1]) + ")=  " + (LaTeX[area]) + ""
textonointZ: "P(Z<x_1)=
P(Z<" + (LaTeX[x_1]) + ")=" + (LaTeX[area]) + ""
textonoint = If(μ ≟ 0 ∧ σ ≟ 1, textonointZ, textonointX)
A: (x_1, 0)
B: (x_2, 0)
C = (3.56, 3.84)
D: (8.26, 3.84)
E: (8.26, 2.28)
F: (3.56, 2.28)
c1, c, d, e, f_1 = Polygon(C, D, E, F)
G = (-3.98, 3.88)
H = (0.52, 3.88)
I = (0.52, 2.34)
J = (-4, 2.34)
c2, g_1, h, i, j = Polygon(G, H, I, J)
Kposicion = (-1.84, 1.92)