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Article Contents

ABSTRACT

1.CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS

1.1. Cumulative Distributions

1.2. Expectation Values

1.3. Distribution Moments. The Mean and Variance

1.4. The Covariance

2. SOME COMMON PROBABILITY DISTRIBUTIONS

2.1. The Binomial Distribution

2.2. The Poisson Distribution

2.3. The Gaussian or Normal Distribution

2.4. The Chi-Square Distribution

3.MEASUREMENT ERRORS AND THE MEASUREMENT PROCESS

3.1. Systematic Errors

3.2. Random Errors

4. SAMPLING AND PARAMETER ESTIMATION. THE MAXIMUM LIKELIHOOD METHOD

4.1. Sample Moments

4.2. The Maximum Likelihood Method

4.3. Estimator for the Poisson Distribution

4.4. Estimators for the Gaussian Distribution

4.5. The Weighted Mean

5. EXAMPLES OF APPLICATIONS

5.1. Mean and Error from a Series of Measurements

5.2. Combining Data with Different Errors

5.3. Determination of Count Rates and Their Errors

5.4. Null Experiments. Setting Confidence Limits When No Counts Are Observed

5.5. Distribution of Time Intervals Between Counts

6.PROPAGATION OF ERRORS

6.1. Examples

7. CURVE FITTING

7.1. The Least Squares Method

7.2. Linear Fits. The Straight Line

7.3. Linear Fits When Both Variables Have Errors

7.4. Nonlinear Fits

8. SOME GENERAL RULES FOR ROUNDING-OFF NUMBERS FOR FINAL PRESENTATION

REFERENCES