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Counting Statistics and Error Prediction

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Presentation on theme: "Counting Statistics and Error Prediction"— Presentation transcript:

1 Counting Statistics and Error Prediction
Chapter3 Counting Statistics and Error Prediction GK-NT-Lec-6-9 Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. 1

2 © 2014 John Wiley & Sons, Inc. All rights reserved.
Lec. No. 6-9 © 2014 John Wiley & Sons, Inc. All rights reserved.

3 © 2014 John Wiley & Sons, Inc. All rights reserved.
Statistical Models 70 I. Characterization of Data 66 II. Statistical Models 70 III. Applications of Statistical Models 79 IV. Error Propagation 85 v. Optimization of Counting Experiments 92 VI. Limits of Detectability 94 VII. Distribution of Time Intervals © 2014 John Wiley & Sons, Inc. All rights reserved.

4 © 2014 John Wiley & Sons, Inc. All rights reserved.
Lec. No. 6 © 2014 John Wiley & Sons, Inc. All rights reserved.

5 2.8………Statistical Models 70-1-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

6 2.8………Statistical Models 70-2-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

7 2.8………Statistical Models 70-3-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

8 2.8……Examp,,…Statistical Models 70-4-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

9 2.9………Statistical Models -5-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

10 2.9………Statistical Models -6-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

11 2.10…….II. Statistical Models-7-NT
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12 2.10…….II. Statistical Models-8-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

13 2.10…….II. Statistical Models-9-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

14 2.10…….II. Statistical Models-10-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

15 2.10…….II. Statistical Models-11-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

16 © 2014 John Wiley & Sons, Inc. All rights reserved.
Lec. No. 7 © 2014 John Wiley & Sons, Inc. All rights reserved.

17 2.10…….II. Statistical Models-11-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

18 2.10…….II. Statistical Models-12-NTN

19 2.10…….II. Statistical Models-13-NTN
© 2014 John Wiley & Sons, Inc. All rights reserved.

20 2.10…….II. Statistical Models-14-NT-New
© 2014 John Wiley & Sons, Inc. All rights reserved.

21 2.10…….II. Statistical Models-15-NT-New
© 2014 John Wiley & Sons, Inc. All rights reserved.

22 2.10…….II. Statistical Models-16-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

23 2.10…….II. Statistical Models-17-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

24 2.11 THE LORENTZIAN DISTRIBUTION-NT-18
© 2014 John Wiley & Sons, Inc. All rights reserved.

25 2.10…….II. Statistical Models-18-NT
© 2014 John Wiley & Sons, Inc. All rights reserved.

26 © 2014 John Wiley & Sons, Inc. All rights reserved.
Lec. No. 8 © 2014 John Wiley & Sons, Inc. All rights reserved.

27 2.12 THE STANDARD, PROBABLE, AND OTHER ERRORS-NT-19
© 2014 John Wiley & Sons, Inc. All rights reserved.

28 2.12 THE STANDARD, PROBABLE, AND OTHER ERRORS-NT-20
© 2014 John Wiley & Sons, Inc. All rights reserved.

29 2.13 THE ARITHMETIC MEAN AND ITS STANDARD ERROR NT-21
© 2014 John Wiley & Sons, Inc. All rights reserved.

30 2.13 THE ARITHMETIC MEAN AND ITS STANDARD ERROR NT-22
© 2014 John Wiley & Sons, Inc. All rights reserved.

31 2.13 THE ARITHMETIC MEAN AND ITS STANDARD ERROR NT-23
© 2014 John Wiley & Sons, Inc. All rights reserved.

32 2.13 THE ARITHMETIC MEAN AND ITS STANDARD ERROR NT-24
© 2014 John Wiley & Sons, Inc. All rights reserved.

33 2.14 CONFIDENCE LIMITS-NT-25
© 2014 John Wiley & Sons, Inc. All rights reserved.

34 © 2014 John Wiley & Sons, Inc. All rights reserved.

35 2.14 CONFIDENCE LIMITS-NT-27
© 2014 John Wiley & Sons, Inc. All rights reserved.

36 2.14 CONFIDENCE LIMITS-NT-28
© 2014 John Wiley & Sons, Inc. All rights reserved.

37 2.14 CONFIDENCE LIMITS-NT-29
© 2014 John Wiley & Sons, Inc. All rights reserved.

38 © 2014 John Wiley & Sons, Inc. All rights reserved.
Lec. No. 9 © 2014 John Wiley & Sons, Inc. All rights reserved.

39 III. APPLICATIONS OF STATISTICAL MODELS-GK-30
© 2014 John Wiley & Sons, Inc. All rights reserved.

40 III. APPLICATIONS OF STATISTICAL MODELS-GK-32
© 2014 John Wiley & Sons, Inc. All rights reserved.

41 III. APPLICATIONS OF STATISTICAL MODELS-GK-33
© 2014 John Wiley & Sons, Inc. All rights reserved.

42 III. APPLICATIONS OF STATISTICAL MODELS-GK-34
© 2014 John Wiley & Sons, Inc. All rights reserved.

43 III. APPLICATIONS OF STATISTICAL MODELS-GK-35
© 2014 John Wiley & Sons, Inc. All rights reserved.

44 III. APPLICATIONS OF STATISTICAL MODELS-GK-36
© 2014 John Wiley & Sons, Inc. All rights reserved.

45 © 2014 John Wiley & Sons, Inc. All rights reserved.

46 III. APPLICATIONS OF STATISTICAL MODELS-GK-reduced-2-37
2/,  is statistical degrees of freedom(N-1) © 2014 John Wiley & Sons, Inc. All rights reserved.

47 III. APPLICATIONS OF STATISTICAL MODELS-GK-reduced-2-38
2/,  is statistical degrees of freedom (N-1) © 2014 John Wiley & Sons, Inc. All rights reserved.

48 III. Application A-APPLICATIONS OF STATISTICAL MODELS-GK-39
© 2014 John Wiley & Sons, Inc. All rights reserved.

49 III. Application B-APPLICATIONS OF STATISTICAL MODELS-GK-40
© 2014 John Wiley & Sons, Inc. All rights reserved.

50 III. Application B-APPLICATIONS OF STATISTICAL MODELS-GK-42-1
© 2014 John Wiley & Sons, Inc. All rights reserved.

51 III. Application B-APPLICATIONS OF STATISTICAL MODELS-GK-41
© 2014 John Wiley & Sons, Inc. All rights reserved.

52 III. Application B-APPLICATIONS OF STATISTICAL MODELS-GK-42
© 2014 John Wiley & Sons, Inc. All rights reserved.

53 III. Application B-APPLICATIONS OF STATISTICAL MODELS-GK-43
© 2014 John Wiley & Sons, Inc. All rights reserved.

54 III. Application B-APPLICATIONS OF STATISTICAL MODELS-GK-44
© 2014 John Wiley & Sons, Inc. All rights reserved.

55 2.16 GOODNESS OF DATA-2 CRITERION-REJECTION OF DATA-NT-44
© 2014 John Wiley & Sons, Inc. All rights reserved.

56 2.16 GOODNESS OF DATA-2 CRITERION-REJECTION OF DATA-NT-45
© 2014 John Wiley & Sons, Inc. All rights reserved.

57 2.16 GOODNESS OF DATA-2 CRITERION-REJECTION OF DATA-NT-46
© 2014 John Wiley & Sons, Inc. All rights reserved.

58 2.16 GOODNESS OF DATA-2 CRITERION-REJECTION OF DATA-NT-46
© 2014 John Wiley & Sons, Inc. All rights reserved.

59 2.16 GOODNESS OF DATA-2 CRITERION-REJECTION OF DATA-NT-47
© 2014 John Wiley & Sons, Inc. All rights reserved.

60 2.16 GOODNESS OF DATA-2 CRITERION-REJECTION OF DATA-NT-50
© 2014 John Wiley & Sons, Inc. All rights reserved.

61 © 2014 John Wiley & Sons, Inc. All rights reserved.

62 © 2014 John Wiley & Sons, Inc. All rights reserved.

63 © 2014 John Wiley & Sons, Inc. All rights reserved.

64 © 2014 John Wiley & Sons, Inc. All rights reserved.

65 © 2014 John Wiley & Sons, Inc. All rights reserved.
Example Poisson Distribution © 2014 John Wiley & Sons, Inc. All rights reserved.

66 © 2014 John Wiley & Sons, Inc. All rights reserved.

67 © 2014 John Wiley & Sons, Inc. All rights reserved.

68 © 2014 John Wiley & Sons, Inc. All rights reserved.

69 © 2014 John Wiley & Sons, Inc. All rights reserved.

70 © 2014 John Wiley & Sons, Inc. All rights reserved.

71 © 2014 John Wiley & Sons, Inc. All rights reserved.

72 Gaussian Probability Distribution Graphs
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73 © 2014 John Wiley & Sons, Inc. All rights reserved.

74

75 © 2014 John Wiley & Sons, Inc. All rights reserved.

76 © 2014 John Wiley & Sons, Inc. All rights reserved.

77 © 2014 John Wiley & Sons, Inc. All rights reserved.


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