Ina

Simon

Andreas

Martina

Gwen

Jan

Johann

Christian

Johann

Tobias

Bastian

Anja

Debora

Sebastian

Wilfried

Simon

Jörg

Christian

Gwen

Markus

Andrea

Daniel

Olaf

Julia

Miriam

Hanna

Sandra

Katrin

Eva

Verena

Jörg

Tiina

Dirk

Marc

Vera

Karoline

Doris

Helen

Sabine

Kathleen

Uwe

Dorothea

1+6

2+3

4+5

Summe

rel. H.

Wahrschlk.

p_{12}

p_6

chi-6

chi-3

1+2+3

f(x)=\frac{1}{2\pi}(1+k\!\cdot \! \sin x)
\text{ ist eine Wahrscheinlichdichte}\
\text{über dem Intervall } [0;2\pi].
\text{ Sie liefert durch Integrieren}\
\text{Wahrscheinlichkeiten für die 6 Felder eines Glücksrades,}\
\text{bei dem eine Haarklemme im Uhrzeigersinn um einen Pin}\
\text{rotiert.}\
\text{Das Glücksrad liegt auf einer schiefen Ebene, Feld 1 oben}\
\text{(bei } x=π \text{), Feld 6 unten bei } x=0 \text{ bzw. } 2\pi.\
\text{Durch Variieren von k passt man das Wahrscheinlichkeits-}\
\text{modell den beobachteten Häufigkeiten an, die in der Tabelle}\
\text{festgehalten werden. Die Abweichungen zwischen Modell}\
\text{und Wirklichkeit werden gemessen durch die } \chi^2 \text{-Testgröße.}

Steigung 10%

Σ

Info

B1: 1
H: B45:G45
C1: 2
D1: 3
E1: 4
F1: 5
G1: 6
B2: 15
C2: 21
D2: 11
E2: 20
F2: 15
G2: 19
B3: 25
C3: 23
D3: 7
E3: 8
F3: 27
G3: 15
B4: 14
C4: 23
D4: 12
E4: 20
F4: 9
G4: 10
B5: 25
C5: 35
D5: 7
E5: 20
F5: 8
G5: 8
B6: 15
C6: 36
D6: 4
E6: 26
F6: 8
G6: 12
B7: 11
C7: 26
D7: 11
E7: 25
F7: 9
G7: 18
B8: 14
C8: 23
D8: 11
E8: 24
F8: 9
G8: 19
B9: 17
C9: 22
D9: 9
E9: 22
F9: 9
G9: 21
B10: 24
C10: 21
D10: 10
E10: 23
F10: 7
G10: 15
B11: 18
C11: 22
D11: 13
E11: 20
F11: 13
G11: 15
B12: 16
C12: 16
D12: 13
E12: 22
F12: 7
G12: 11
B13: 11
C13: 22
D13: 11
E13: 21
F13: 10
G13: 27
B14: 14
C14: 17
D14: 11
E14: 24
F14: 6
G14: 12
B15: 17
C15: 19
D15: 8
E15: 14
F15: 6
G15: 20
B16: 14
C16: 27
D16: 11
E16: 28
F16: 11
G16: 13
B17: 25
C17: 23
D17: 5
E17: 27
F17: 8
G17: 15
B18: 10
C18: 24
D18: 12
E18: 27
F18: 7
G18: 12
B19: 17
C19: 22
D19: 9
E19: 22
F19: 9
G19: 21
B20: 21
C20: 20
D20: 8
E20: 22
F20: 11
G20: 18
B21: 15
C21: 31
D21: 7
E21: 20
F21: 6
G21: 11
B22: 17
C22: 20
D22: 11
E22: 28
F22: 10
G22: 19
B23: 20
C23: 17
D23: 12
E23: 26
F23: 11
G23: 14
B24: 19
C24: 25
D24: 10
E24: 25
F24: 13
G24: 21
B25: 11
C25: 19
D25: 12
E25: 32
F25: 10
G25: 16
B26: 17
C26: 29
D26: 11
E26: 25
F26: 3
G26: 15
B27: 19
C27: 24
D27: 12
E27: 24
F27: 6
G27: 15
B28: 18
C28: 20
D28: 15
E28: 24
F28: 5
G28: 18
B29: 16
C29: 27
D29: 4
E29: 22
F29: 11
G29: 20
B30: 19
C30: 32
D30: 9
E30: 26
F30: 5
G30: 9
B31: 19
C31: 17
D31: 11
E31: 30
F31: 11
G31: 17
B32: 24
C32: 17
D32: 8
E32: 20
F32: 15
G32: 16
B33: 17
C33: 29
D33: 12
E33: 21
F33: 8
G33: 14
B34: 19
C34: 19
D34: 6
E34: 30
F34: 7
G34: 19
B35: 20
C35: 18
D35: 10
E35: 18
F35: 11
G35: 23
B36: 15
C36: 29
D36: 14
E36: 22
F36: 8
G36: 12
B37: 15
C37: 23
D37: 11
E37: 32
F37: 6
G37: 13
B38: 16
C38: 24
D38: 7
E38: 28
F38: 11
G38: 14
B39: 17
C39: 24
D39: 8
E39: 22
F39: 13
G39: 16
B40: 11
C40: 22
D40: 12
E40: 30
F40: 11
G40: 14
B41: 19
C41: 19
D41: 8
E41: 28
F41: 13
G41: 18
B42: 13
C42: 20
D42: 10
E42: 25
F42: 12
G42: 20
B43: 7
C43: 20
D43: 15
E43: 25
F43: 15
G43: 18
H2 = Sum(B2:G2)
H3 = Sum(B3:G3)
H4 = Sum(B4:G4)
H5 = Sum(B5:G5)
H6 = Sum(B6:G6)
H7 = Sum(B7:G7)
H8 = Sum(B8:G8)
H9 = Sum(B9:G9)
H10 = Sum(B10:G10)
H11 = Sum(B11:G11)
H12 = Sum(B12:G12)
H13 = Sum(B13:G13)
H14 = Sum(B14:G14)
H15 = Sum(B15:G15)
H16 = Sum(B16:G16)
H17 = Sum(B17:G17)
H18 = Sum(B18:G18)
H19 = Sum(B19:G19)
H20 = Sum(B20:G20)
H21 = Sum(B21:G21)
H22 = Sum(B22:G22)
H23 = Sum(B23:G23)
H24 = Sum(B24:G24)
H25 = Sum(B25:G25)
H26 = Sum(B26:G26)
H27 = Sum(B27:G27)
H28 = Sum(B28:G28)
H29 = Sum(B29:G29)
H30 = Sum(B30:G30)
H31 = Sum(B31:G31)
H32 = Sum(B32:G32)
H33 = Sum(B33:G33)
H34 = Sum(B34:G34)
H35 = Sum(B35:G35)
H36 = Sum(B36:G36)
H37 = Sum(B37:G37)
H38 = Sum(B38:G38)
H39 = Sum(B39:G39)
H40 = Sum(B40:G40)
H41 = Sum(B41:G41)
H42 = Sum(B42:G42)
H43 = Sum(B43:G43)
J2: B2 + G2
K2: C2 + D2
L2: E2 + F2
J3: B3 + G3
K3: C3 + D3
L3: E3 + F3
J4: B4 + G4
K4: C4 + D4
L4: E4 + F4
J5: B5 + G5
K5: C5 + D5
L5: E5 + F5
J6: B6 + G6
K6: C6 + D6
L6: E6 + F6
J7: B7 + G7
K7: C7 + D7
L7: E7 + F7
J8: B8 + G8
K8: C8 + D8
L8: E8 + F8
J9: B9 + G9
K9: C9 + D9
L9: E9 + F9
J10: B10 + G10
K10: C10 + D10
L10: E10 + F10
J11: B11 + G11
K11: C11 + D11
L11: E11 + F11
J12: B12 + G12
K12: C12 + D12
L12: E12 + F12
J13: B13 + G13
K13: C13 + D13
L13: E13 + F13
J14: B14 + G14
K14: C14 + D14
L14: E14 + F14
J15: B15 + G15
K15: C15 + D15
L15: E15 + F15
J16: B16 + G16
K16: C16 + D16
L16: E16 + F16
J17: B17 + G17
K17: C17 + D17
L17: E17 + F17
J18: B18 + G18
K18: C18 + D18
L18: E18 + F18
J19: B19 + G19
K19: C19 + D19
L19: E19 + F19
J20: B20 + G20
K20: C20 + D20
L20: E20 + F20
J21: B21 + G21
K21: C21 + D21
L21: E21 + F21
J22: B22 + G22
K22: C22 + D22
L22: E22 + F22
J23: B23 + G23
K23: C23 + D23
L23: E23 + F23
J24: B24 + G24
K24: C24 + D24
L24: E24 + F24
J25: B25 + G25
K25: C25 + D25
L25: E25 + F25
J26: B26 + G26
K26: C26 + D26
L26: E26 + F26
J27: B27 + G27
K27: C27 + D27
L27: E27 + F27
J28: B28 + G28
K28: C28 + D28
L28: E28 + F28
J29: B29 + G29
K29: C29 + D29
L29: E29 + F29
J30: B30 + G30
K30: C30 + D30
L30: E30 + F30
J31: B31 + G31
K31: C31 + D31
L31: E31 + F31
J32: B32 + G32
K32: C32 + D32
L32: E32 + F32
J33: B33 + G33
K33: C33 + D33
L33: E33 + F33
J34: B34 + G34
K34: C34 + D34
L34: E34 + F34
J35: B35 + G35
K35: C35 + D35
L35: E35 + F35
J36: B36 + G36
K36: C36 + D36
L36: E36 + F36
J37: B37 + G37
K37: C37 + D37
L37: E37 + F37
J38: B38 + G38
K38: C38 + D38
L38: E38 + F38
J39: B39 + G39
K39: C39 + D39
L39: E39 + F39
J40: B40 + G40
K40: C40 + D40
L40: E40 + F40
J41: B41 + G41
K41: C41 + D41
L41: E41 + F41
J42: B42 + G42
K42: C42 + D42
L42: E42 + F42
J43: B43 + G43
K43: C43 + D43
L43: E43 + F43
B45 = Sum(B2:B43)
C45 = Sum(C2:C43)
D45 = Sum(D2:D43)
E45 = Sum(E2:E43)
F45 = Sum(F2:F43)
G45 = Sum(G2:G43)
H45 = Sum(H2:H43)
J45 = Sum(J2:J43)
K45 = Sum(K2:K43)
L45 = Sum(L2:L43)
B46: B45 / $H45
C46: C45 / $H45
D46: D45 / $H45
E46: E45 / $H45
F46: F45 / $H45
G46: G45 / $H45
J46: (J45 / $H45 * 100)
K46: (K45 / $H45 * 100)
L46: (L45 / $H45 * 100)
A = Point(xAxis)
B = Intersect(xAxis, yAxis)
Vieleck1, o, g, h, i, j, k_{1}, C, D, E, F = Polygon(A, B, 6)
l = Segment(B, E)
n = Sum(H)
m = Segment(C, F)
G = Intersect(l, m)
c = Circle(G, F)
Text7: "n = " + H45 + ""
k = 0.53 (slider from 0 to 1, step 0.01)
f(x) = If[0 ≤ x ≤ 6.283185307179586, (1 + (k * sin(x))) / ((2 * pi))]
w = Sequence(Integral[f, ((i * 2) * pi / 12), (((i + 1) * 2) * pi / 12)], i, 0, 11)
p: {w(6) + w(7), w(4) + w(5), w(8) + w(9), w(2) + w(3), w(10) + w(11), w(1) + w(12)}
B47: p(1)
C47: p(2)
D47: p(3)
E47: p(4)
F47: p(5)
G47: p(6)
chiq = Sum(Sequence[((n * p(i)) - H(i))^(2) / ((n * p(i))), i, 1, 6])
CHI: (7, chiq / 100)
Text8: "Χ² = " + chiq + ""
q = Segment(A, D)
C50: w(6)
D50: w(7)
E51: w(8)
F52: w(9)
F53: w(10)
E54: w(11)
D55: w(12)
C55: w(1)
B54: w(2)
A53: w(3)
A52: w(4)
B51: w(5)
Text9: "" + (w(1)) + ""
Text10: "" + (w(2)) + ""
Text11: "" + (w(3)) + ""
Text12: "" + (w(4)) + ""
Text13: "" + (w(5)) + ""
Text14: "" + (w(6)) + ""
Text15: "" + (w(7)) + ""
Text16: "" + (w(8)) + ""
Text17: "" + (w(9)) + ""
Text18: "" + (w(10)) + ""
Text19: "" + (w(11)) + ""
Text20: "" + (w(12)) + ""
a = false
b = true
Text21: "" + (p(1)) + ""
Text22: "" + (p(2)) + ""
Text23: "" + (p(3)) + ""
Text24: "" + (p(4)) + ""
Text25: "" + (p(5)) + ""
Text26: "" + (p(6)) + ""
M3: Sum[(B3:G3 - H3 / 6)^(2)] / (H3 / 6)
M4: Sum[(B4:G4 - H4 / 6)^(2)] / (H4 / 6)
M5: Sum[(B5:G5 - H5 / 6)^(2)] / (H5 / 6)
M6: Sum[(B6:G6 - H6 / 6)^(2)] / (H6 / 6)
M7: Sum[(B7:G7 - H7 / 6)^(2)] / (H7 / 6)
M8: Sum[(B8:G8 - H8 / 6)^(2)] / (H8 / 6)
N2: Sum[(J2:L2 - H2 / 3)^(2)] / (H2 / 3)
N3: Sum[(J3:L3 - H3 / 3)^(2)] / (H3 / 3)
N4: Sum[(J4:L4 - H4 / 3)^(2)] / (H4 / 3)
N5: Sum[(J5:L5 - H5 / 3)^(2)] / (H5 / 3)
N6: Sum[(J6:L6 - H6 / 3)^(2)] / (H6 / 3)
N7: Sum[(J7:L7 - H7 / 3)^(2)] / (H7 / 3)
N8: Sum[(J8:L8 - H8 / 3)^(2)] / (H8 / 3)
M9: Sum[(B9:G9 - H9 / 6)^(2)] / (H9 / 6)
M10: Sum[(B10:G10 - H10 / 6)^(2)] / (H10 / 6)
M11: Sum[(B11:G11 - H11 / 6)^(2)] / (H11 / 6)
M12: Sum[(B12:G12 - H12 / 6)^(2)] / (H12 / 6)
M13: Sum[(B13:G13 - H13 / 6)^(2)] / (H13 / 6)
M14: Sum[(B14:G14 - H14 / 6)^(2)] / (H14 / 6)
M15: Sum[(B15:G15 - H15 / 6)^(2)] / (H15 / 6)
M16: Sum[(B16:G16 - H16 / 6)^(2)] / (H16 / 6)
M17: Sum[(B17:G17 - H17 / 6)^(2)] / (H17 / 6)
M18: Sum[(B18:G18 - H18 / 6)^(2)] / (H18 / 6)
M19: Sum[(B19:G19 - H19 / 6)^(2)] / (H19 / 6)
M20: Sum[(B20:G20 - H20 / 6)^(2)] / (H20 / 6)
M21: Sum[(B21:G21 - H21 / 6)^(2)] / (H21 / 6)
M22: Sum[(B22:G22 - H22 / 6)^(2)] / (H22 / 6)
M23: Sum[(B23:G23 - H23 / 6)^(2)] / (H23 / 6)
M24: Sum[(B24:G24 - H24 / 6)^(2)] / (H24 / 6)
M25: Sum[(B25:G25 - H25 / 6)^(2)] / (H25 / 6)
M26: Sum[(B26:G26 - H26 / 6)^(2)] / (H26 / 6)
M27: Sum[(B27:G27 - H27 / 6)^(2)] / (H27 / 6)
M28: Sum[(B28:G28 - H28 / 6)^(2)] / (H28 / 6)
M29: Sum[(B29:G29 - H29 / 6)^(2)] / (H29 / 6)
M30: Sum[(B30:G30 - H30 / 6)^(2)] / (H30 / 6)
M31: Sum[(B31:G31 - H31 / 6)^(2)] / (H31 / 6)
M32: Sum[(B32:G32 - H32 / 6)^(2)] / (H32 / 6)
M33: Sum[(B33:G33 - H33 / 6)^(2)] / (H33 / 6)
M34: Sum[(B34:G34 - H34 / 6)^(2)] / (H34 / 6)
M35: Sum[(B35:G35 - H35 / 6)^(2)] / (H35 / 6)
M36: Sum[(B36:G36 - H36 / 6)^(2)] / (H36 / 6)
M37: Sum[(B37:G37 - H37 / 6)^(2)] / (H37 / 6)
M38: Sum[(B38:G38 - H38 / 6)^(2)] / (H38 / 6)
M39: Sum[(B39:G39 - H39 / 6)^(2)] / (H39 / 6)
M40: Sum[(B40:G40 - H40 / 6)^(2)] / (H40 / 6)
M41: Sum[(B41:G41 - H41 / 6)^(2)] / (H41 / 6)
M42: Sum[(B42:G42 - H42 / 6)^(2)] / (H42 / 6)
M43: Sum[(B43:G43 - H43 / 6)^(2)] / (H43 / 6)
N9: Sum[(J9:L9 - H9 / 3)^(2)] / (H9 / 3)
N10: Sum[(J10:L10 - H10 / 3)^(2)] / (H10 / 3)
N11: Sum[(J11:L11 - H11 / 3)^(2)] / (H11 / 3)
N12: Sum[(J12:L12 - H12 / 3)^(2)] / (H12 / 3)
N13: Sum[(J13:L13 - H13 / 3)^(2)] / (H13 / 3)
N14: Sum[(J14:L14 - H14 / 3)^(2)] / (H14 / 3)
N15: Sum[(J15:L15 - H15 / 3)^(2)] / (H15 / 3)
N16: Sum[(J16:L16 - H16 / 3)^(2)] / (H16 / 3)
N17: Sum[(J17:L17 - H17 / 3)^(2)] / (H17 / 3)
N18: Sum[(J18:L18 - H18 / 3)^(2)] / (H18 / 3)
N19: Sum[(J19:L19 - H19 / 3)^(2)] / (H19 / 3)
N20: Sum[(J20:L20 - H20 / 3)^(2)] / (H20 / 3)
N21: Sum[(J21:L21 - H21 / 3)^(2)] / (H21 / 3)
N22: Sum[(J22:L22 - H22 / 3)^(2)] / (H22 / 3)
N23: Sum[(J23:L23 - H23 / 3)^(2)] / (H23 / 3)
N24: Sum[(J24:L24 - H24 / 3)^(2)] / (H24 / 3)
N25: Sum[(J25:L25 - H25 / 3)^(2)] / (H25 / 3)
N26: Sum[(J26:L26 - H26 / 3)^(2)] / (H26 / 3)
N27: Sum[(J27:L27 - H27 / 3)^(2)] / (H27 / 3)
N28: Sum[(J28:L28 - H28 / 3)^(2)] / (H28 / 3)
N29: Sum[(J29:L29 - H29 / 3)^(2)] / (H29 / 3)
N30: Sum[(J30:L30 - H30 / 3)^(2)] / (H30 / 3)
N31: Sum[(J31:L31 - H31 / 3)^(2)] / (H31 / 3)
N32: Sum[(J32:L32 - H32 / 3)^(2)] / (H32 / 3)
N33: Sum[(J33:L33 - H33 / 3)^(2)] / (H33 / 3)
N34: Sum[(J34:L34 - H34 / 3)^(2)] / (H34 / 3)
N35: Sum[(J35:L35 - H35 / 3)^(2)] / (H35 / 3)
N36: Sum[(J36:L36 - H36 / 3)^(2)] / (H36 / 3)
N37: Sum[(J37:L37 - H37 / 3)^(2)] / (H37 / 3)
N38: Sum[(J38:L38 - H38 / 3)^(2)] / (H38 / 3)
N39: Sum[(J39:L39 - H39 / 3)^(2)] / (H39 / 3)
N40: Sum[(J40:L40 - H40 / 3)^(2)] / (H40 / 3)
N41: Sum[(J41:L41 - H41 / 3)^(2)] / (H41 / 3)
N42: Sum[(J42:L42 - H42 / 3)^(2)] / (H42 / 3)
N43: Sum[(J43:L43 - H43 / 3)^(2)] / (H43 / 3)
M2: Sum[(B2:G2 - H2 / 6)^(2)] / (H2 / 6)
Text1: "1
" + B46 + ""
Text3: "3
" + D46 + ""
Text5: "5
" + F46 + ""
Text6: "6
" + G46 + ""
Text4: "4
" + E46 + ""
Text2: "2
" + C46 + ""
I2 = Sum(B2:D2)
I3 = Sum(B3:D3)
I4 = Sum(B4:D4)
I5 = Sum(B5:D5)
I6 = Sum(B6:D6)
I7 = Sum(B7:D7)
I8 = Sum(B8:D8)
I9 = Sum(B9:D9)
I10 = Sum(B10:D10)
I11 = Sum(B11:D11)
I12 = Sum(B12:D12)
I13 = Sum(B13:D13)
I14 = Sum(B14:D14)
I15 = Sum(B15:D15)
I16 = Sum(B16:D16)
I17 = Sum(B17:D17)
I18 = Sum(B18:D18)
I19 = Sum(B19:D19)
I20 = Sum(B20:D20)
I21 = Sum(B21:D21)
I22 = Sum(B22:D22)
I23 = Sum(B23:D23)
I24 = Sum(B24:D24)
I25 = Sum(B25:D25)
I26 = Sum(B26:D26)
I27 = Sum(B27:D27)
I28 = Sum(B28:D28)
I29 = Sum(B29:D29)
I30 = Sum(B30:D30)
I31 = Sum(B31:D31)
I32 = Sum(B32:D32)
I33 = Sum(B33:D33)
I34 = Sum(B34:D34)
I35 = Sum(B35:D35)
I36 = Sum(B36:D36)
I37 = Sum(B37:D37)
I38 = Sum(B38:D38)
I39 = Sum(B39:D39)
I40 = Sum(B40:D40)
I41 = Sum(B41:D41)
I42 = Sum(B42:D42)
I43 = Sum(B43:D43)
I45 = Sum(I2:I43)
I46: (I45 / $H45 * 100)
d = Integral(f, pi / 6, (5 * pi / 6))
I = Intersect(l, m)
J = Intersect(c, l, 1)
K = Intersect(c, q, 2)
e = CircleSector(I, J, K)
r = true
Text27: "\chi^2=" + (LaTeX[chiq]) + ""