Diese Grafiksammlung enthält insgesamt 180 Säulendiagramme zur Binomialverteilung. Die Bernoullikettenlänge n umfasst Werte von 1 bis 20. Zu jedem Wert von n gehören Trefferwahrscheinlichkeiten von p = 0,1 bis p = 0,9 mit der Schrittweite 0,1.
Die Grafiken eignen sich in idealer Weise zu vielfältigen und ausführlichen vergleichenden Betrachtungen und Untersuchungen verschiedener Binomialverteilungen.
Einen erfolgreichen Einsatz der Grafiken wünschen Ihnen Autor und Verlag!
Wolfgang Göbels
Grafische Veranschaulichung
der Binomialverteilung
180 Säulendiagramme zur detaillierten Analyse
Diese Grafiksammlung enthält insgesamt 180 Säulendiagramme zur Binomialvertei-
lung. Die Bernoullikettenlänge n umfasst Werte von 1 bis 20. Zu jedem Wert von n
gehören Trefferwahrscheinlichkeiten von p = 0,1 bis p = 0,9 mit der Schrittweite 0,1.
Die Grafiken eignen sich in idealer Weise zu vielfältigen und ausführlichen verglei-
chenden Betrachtungen und Untersuchungen verschiedener Binomialverteilungen.
Einen erfolgreichen Einsatz der Grafiken wünschen Ihnen Autor und Verlag!
1
n=
1
p
=
0,1
k =
0
0,900000
1
0,100000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
0,900000
1,000000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
2
n=
1
p
=
0,2
k =
0
0,800000
1
0,200000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
0,900000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
3
n=
1
p
=
0,3
k =
0
0,700000
1
0,300000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
4
n=
1
p
=
0,4
k =
0
0,600000
1
0,400000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
5
n=
1
p
=
0,5
k =
0
0,500000
1
0,500000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
6
n=
1
p
=
0,6
k =
0
0,400000
1
0,600000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
7
n=
1
p
=
0,7
k =
0
0,300000
1
0,700000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
8
n=
1
p
=
0,8
k =
0
0,200000
1
0,800000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
0,900000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
9
n=
1
p
=
0,9
k =
0
0,100000
1
0,900000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
0,900000
1,000000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
10
n=
2
p
=
0,1
k =
0
0,810000
1
0,180000
2
0,010000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
0,900000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
11
n=
2
p
=
0,2
k =
0
0,640000
1
0,320000
2
0,040000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
12
n=
2
p
=
0,3
k =
0
0,490000
1
0,420000
2
0,090000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
13
n=
2
p
=
0,4
k =
0
0,360000
1
0,480000
2
0,160000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
14
n=
2
p
=
0,5
k =
0
0,250000
1
0,500000
2
0,250000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
15
n=
2
p
=
0,6
k =
0
0,160000
1
0,480000
2
0,360000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
16
n=
2
p
=
0,7
k =
0
0,090000
1
0,420000
2
0,490000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
17
n=
2
p
=
0,8
k =
0
0,040000
1
0,320000
2
0,640000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
18
n=
2
p
=
0,9
k =
0
0,010000
1
0,180000
2
0,810000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
0,900000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
19
n=
3
p
=
0,1
k =
0
0,729000
1
0,243000
2
0,027000
3
0,001000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
20
n=
3
p
=
0,2
k =
0
0,512000
1
0,384000
2
0,096000
3
0,008000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
21
n=
3
p
=
0,3
k =
0
0,343000
1
0,441000
2
0,189000
3
0,027000
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
0,500000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
22
n=
3
p
=
0,4
k =
0
0,216000
1
0,432000
2
0,288000
3
0,064000
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
0,500000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
23
n=
3
p
=
0,5
k =
0
0,125000
1
0,375000
2
0,375000
3
0,125000
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
24
n=
3
p
=
0,6
k =
0
0,064000
1
0,288000
2
0,432000
3
0,216000
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
0,500000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
25
n=
3
p
=
0,7
k =
0
0,027000
1
0,189000
2
0,441000
3
0,343000
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
0,500000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
26
n=
3
p
=
0,8
k =
0
0,008000
1
0,096000
2
0,384000
3
0,512000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
27
n=
3
p
=
0,9
k =
0
0,001000
1
0,027000
2
0,243000
3
0,729000
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
0,800000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
28
n=
4
p
=
0,1
k =
0
0,656100
1
0,291600
2
0,048600
3
0,003600
4
0,000100
Binomialverteilung
0,000000
0,100000
0,200000
0,300000
0,400000
0,500000
0,600000
0,700000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
29
n=
4
p
=
0,2
k =
0
0,409600
1
0,409600
2
0,153600
3
0,025600
4
0,001600
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
30
n=
4
p
=
0,3
k =
0
0,240100
1
0,411600
2
0,264600
3
0,075600
4
0,008100
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
31
n=
4
p
=
0,4
k =
0
0,129600
1
0,345600
2
0,345600
3
0,153600
4
0,025600
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
32
n=
4
p
=
0,5
k =
0
0,062500
1
0,250000
2
0,375000
3
0,250000
4
0,062500
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
33
n=
4
p
=
0,6
k =
0
0,025600
1
0,153600
2
0,345600
3
0,345600
4
0,129600
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
34
n=
4
p
=
0,7
k =
0
0,008100
1
0,075600
2
0,264600
3
0,411600
4
0,240100
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
35
n=
4
p
=
0,8
k =
0
0,001600
1
0,025600
2
0,153600
3
0,409600
4
0,409600
Binomialverteilung
0,000000
0,050000
0,100000
0,150000
0,200000
0,250000
0,300000
0,350000
0,400000
0,450000
01
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
k
P(X=
k)
36
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- Quote paper
- Diplom-Mathematiker Wolfgang Göbels (Author), 2013, Grafische Veranschaulichung der Binomialverteilung: 180 Säulendiagramme zur detaillierten Analyse, Munich, GRIN Verlag, https://www.grin.com/document/211878
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Upload your own papers! Earn money and win an iPhone X. -
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Upload your own papers! Earn money and win an iPhone X. -
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Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
-
Upload your own papers! Earn money and win an iPhone X. -
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Upload your own papers! Earn money and win an iPhone X.