f_é

Valeur de p

n = 40 (slider from 30 to 100, step 5)
f(x) = (x + 1.96^(2.0) / (2.0 * n) - 1.96 * sqrt(1.96^(2.0) / (4.0 * n^(2.0)) + x * (1.0 - x) / n)) / (1.0 + 1.96^(2.0) / n)
g(x) = (x + 1.96^(2.0) / (2.0 * n) + 1.96 * sqrt(1.96^(2.0) / (4.0 * n^(2.0)) + x * (1.0 - x) / n)) / (1.0 + 1.96^(2.0) / n)
A1 = 0.1
A2 = 0.15
A3: 2.0 * A2 - A1
A4: 2.0 * A3 - A2
A5: 2.0 * A4 - A3
A6: 2.0 * A5 - A4
A7: 2.0 * A6 - A5
A8: 2.0 * A7 - A6
A9: 2.0 * A8 - A7
A10: 2.0 * A9 - A8
A11: 2.0 * A10 - A9
A12: 2.0 * A11 - A10
A13: 2.0 * A12 - A11
A14: 2.0 * A13 - A12
A15: 2.0 * A14 - A13
A16: 2.0 * A15 - A14
A17: 2.0 * A16 - A15
A18: 2.0 * A17 - A16
B1(x) = A1
B2(x) = A2
B3(x) = A3
B4(x) = A4
B5(x) = A5
B6(x) = A6
B7(x) = A7
B8(x) = A8
B9(x) = A9
B10(x) = A10
B11(x) = A11
B12(x) = A12
B13(x) = A13
B14(x) = A14
B15(x) = A15
B16(x) = A16
B17(x) = A17
B18(x) = A18
D1 = Intersect(g(x), B1, (0.007029036791040882, 0.09999999999998506))
D2 = Intersect(g(x), B2, (0.03934241249204035, 0.1499999891419784))
D3 = Intersect(g(x), B3, (0.07603871323057314, 0.19999999675493055))
D4 = Intersect(g(x), B4, (0.11580797226403937, 0.24999999860281738))
D5 = Intersect(g(x), B5, (0.15798450724284607, 0.29999999925469845))
D6 = Intersect(g(x), B6, (0.2021855889221468, 0.349999999541661))
D7 = Intersect(g(x), B7, (0.24817905253602096, 0.39999999968758904))
D8 = Intersect(g(x), B8, (0.2958250990955882, 0.44999999976941873))
D9 = Intersect(g(x), B9, (0.3450483944701011, 0.49999999981835175))
D10 = Intersect(g(x), B10, (0.39582509916287706, 0.5499999998486047))
D11 = Intersect(g(x), B11, (0.44817905268742836, 0.5999999998671623))
D12 = Intersect(g(x), B12, (0.5021855892013898, 0.6499999998775114))
D13 = Intersect(g(x), B13, (0.5579845077524075, 0.6999999998811401))
D14 = Intersect(g(x), B14, (0.6158079732673878, 0.7499999998779847))
D15 = Intersect(g(x), B15, (0.6760387155562814, 0.7999999998660221))
D16 = Intersect(g(x), B16, (0.7393424198420928, 0.8499999998391795))
D17 = Intersect(g(x), B17, (0.8070290364787963, 0.8999999997790459))
D18 = Intersect(g(x), B18, (0.8824581604722451, 0.9499999996081929))
C1 = Intersect(f(x), B1, (0.19297096352120233, 0.10000000022095318))
C2 = Intersect(f(x), B2, (0.260657580157906, 0.15000000016081963))
C3 = Intersect(f(x), B3, (0.32396128444371763, 0.2000000001339772))
C4 = Intersect(f(x), B4, (0.38419202673261127, 0.25000000012201445))
C5 = Intersect(f(x), B5, (0.44201549224759173, 0.30000000011885924))
C6 = Intersect(f(x), B6, (0.4978144107986096, 0.35000000012248805))
C7 = Intersect(f(x), B7, (0.5518209473125709, 0.40000000013283704))
C8 = Intersect(f(x), B8, (0.6041749008371221, 0.4500000001513944))
C9 = Intersect(f(x), B9, (0.6549516055298982, 0.5000000001816476))
C10 = Intersect(f(x), B10, (0.704174900904411, 0.5500000002305806))
C11 = Intersect(f(x), B11, (0.7518209474639784, 0.6000000003124104))
C12 = Intersect(f(x), B12, (0.7978144110778527, 0.6500000004583385))
C13 = Intersect(f(x), B13, (0.8420154927571533, 0.7000000007453009))
C14 = Intersect(f(x), B14, (0.8841920277359601, 0.7500000013971819))
C15 = Intersect(f(x), B15, (0.9239612867694262, 0.8000000032450687))
C16 = Intersect(f(x), B16, (0.9606575875079589, 0.8500000108580207))
C17 = Intersect(f(x), B17, (0.9929709632089585, 0.9000000000000139))
C18 = Intersect(f(x), B18, (1.0279905977239134, 0.9499999999999988))
E1 = Segment(C1, D1)
E2 = Segment(C2, D2)
E3 = Segment(C3, D3)
E4 = Segment(C4, D4)
E5 = Segment(C5, D5)
E6 = Segment(C6, D6)
E7 = Segment(C7, D7)
E8 = Segment(C8, D8)
E9 = Segment(C9, D9)
E10 = Segment(C10, D10)
E11 = Segment(C11, D11)
E12 = Segment(C12, D12)
E13 = Segment(C13, D13)
E14 = Segment(C14, D14)
E15 = Segment(C15, D15)
E16 = Segment(C16, D16)
E17 = Segment(C17, D17)
E18 = Segment(C18, D18)
f_é = 0.65 (slider from 0 to 1, step 0.025)
a: x = f_é
A = Intersect(f, a, (0.65, 0.4950559699353738))
B = Intersect(g, a, (0.65, 0.7786566682895085))
C: (0.0, y(A))
D: (0.0, y(B))
b = Segment(D, C)
c = Segment(B, A)
E: (x(A), 0.0)
d = Segment(A, E)
e = Segment(B, D)
h = Segment(A, C)
p = 0.6
F: (0.0, p)
G: (1.0, p)
i = Segment(F, G)
j = Segment(D, C)
k = false
H = Intersect(g, i, (0.44817905268742886, 0.5999999998671628))
I = Intersect(f, i, (0.7518209474639788, 0.6000000003124107))
J: (x(H), 0.0)
K: (x(I), 0.0)
l = Segment(J, K)
m = Segment(H, I)
f_1 = Function(f, 0.0, 1.0)
g_1 = Function(g, 0.0, 1.0)