常態分配
Author: 藍邦偉  老師

(μ,0)

(μ+σ,0)

(μ-σ,0)

(μ+2σ,0)

(μ+3σ,0)

(μ-3σ,0)

()

(μ-2σ)

68%

95%

99.7%

常態分配

μ = 0 (slider from -4 to 4, step 0.5)
σ = 0.7 (slider from 0.3 to 2, step 0.1)
f(x) = 1 / ((2 * 3.141592653589793)^(1 / 2) * σ) * exp((-(x - μ)^(2)) / 2 * σ^(2))
F_0: (μ, f(μ))
F_1: (μ, 0)
n = Segment(F_0, F_1)
F_2: (μ + σ, f(μ + σ))
F_3: (μ + σ, 0)
F_4: (μ - σ, f(μ - σ))
F_5: (μ - σ, 0)
F_6: (μ + 2 * σ, f(μ + 2 * σ))
F_7: (μ + 2 * σ, 0)
F_8: (μ + 3 * σ, f(μ + 3 * σ))
F_9: (μ + 3 * σ, 0)
F_{11}: (μ - 3 * σ, 0)
F_{10}: (μ - 3 * σ, f(μ - 3 * σ))
F_{12}: (μ - 2 * σ, f(μ - 2 * σ))
F_{13}: (μ - 2 * σ, 0)
a = Segment(F_4, F_5)
b = Segment(F_{12}, F_{13})
c = Segment(F_2, F_3)
d = Segment(F_6, F_7)
e = Integral(f, μ - σ, μ + σ)
g = false
h = Integral(f, μ - 2 * σ, μ + 2 * σ)
i = false
j = Integral(f, μ - 3 * σ, μ + 3 * σ)
k = true
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
l = Segment(F_8, F_9)
m = Segment(F_{10}, F_{11})