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    -

    -

    0

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    0.1

    0.15

    0.2

    0.25

    0.3

    0.35

    0.4

    0.45

    -1 -0.5 0 0.5 1 1.5 2

    x

    -

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    0

    50

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    200

    0 50 100 150 200 250 300

    A

    ngle

    Trial number

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    0

    0.001

    0.002

    0.003

    0.004

    0.005

    0.006

    0.007

    0.008

    0.009

    0.01

    0 50 100 150 200

    Probability

    Angle

    0

    20

    40

    60

    80

    100

    120

    140

    160

    180

    0 100 200 300 400 500 600 700 800 900 1 000

    Angle

    Trial number

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    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0 50 100 150 200

    Cumulativeprobability

    Angle

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    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0 1 2 3 4 5 6 7 8

    Cumulativeprobability

    Die number

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    -

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    0

    0.05

    0.1

    0.15

    0.2

    0.25

    0.3

    0.35

    0.4

    0 2 4 6 8 10

    Probability

    Mean expected

    k = 1

    k = 2

    k = 5

    k = 8

    -

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    0

    0.05

    0.1

    0.15

    0.2

    0.25

    0.3

    0.35

    0.4

    -10 -5 0 5 10

    Probability

    x

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    0

    0.2

    0.4

    0.6

    0.8

    1

    -6 -4 -2 0 2 4 6

    Frequency

    x

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    1

    1.5

    2

    2.5

    3

    3.5

    4

    0 0.5 1 1.5 2

    y

    x

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    -0.5

    0

    0.5

    1

    1.5

    2

    2.5

    3

    3.5

    -1.5 -1 -0.5 0 0.5 1 1.5

    y

    x

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    0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    2 3 4 5 6 7 8

    Likelih

    oodofxbeingtrue

    x

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    -11

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    -9

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    -7

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    -5

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    -2

    2 3 4 5 6 7 8

    Loglikelihood

    x

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    0

    0.05

    0.1

    0.15

    0.2

    0.25

    0.3

    0.35

    0.4

    0 2 4 6 8 10 12 14

    Probability

    Chi squared

    nu = 1

    nu = 3

    nu = 6

    nu = 10nu = 20

    -

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    0

    0.2

    0.4

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    0.8

    1

    0 0.5 1 1.5 2 2.5 3

    Confidencelevel

    Reduced chi squared

    nu = 1

    nu = 100

    Intermediate lines, in order:nu = 3, 6, 10, 20

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    0

    50

    100

    150

    200

    0 0.2 0.4 0.6 0.8 1

    Numberofevents

    Confidence level

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    -10 -50 5 10

    15 20 -20-15

    -10-5

    05

    10

    0

    500

    1000

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    25

    30

    35

    40

    45

    50

    55

    60

    65

    70

    75

    16 18 20 22 24

    b

    a

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    0

    5

    10

    15

    20

    25

    30

    35

    40

    -5 0 5 10 15

    Chisquared

    a

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    -0.8

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    0

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    0.8

    1

    -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

    y

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    0

    5000

    10000

    15000

    20000

    25000

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

    y

    x

    2.4% of eventshave R > 0.44

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