The Gaussian Limit
Statistics and Data Analysis
Prof. dr hab. Elżbieta Richter-Wąs
Follow the course/slides from M. A. Thomson lectures at Cambridge University
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3
The Central Limit Theorem
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A useful integral relationship
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Properties of Gaussian Distribution
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Properties of the 1D Gaussian Distribution, cont.
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Averaging Gaussian Measurements
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Averaging Gaussian Measurements II
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Error Propagation I
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Error on Error
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Combining Gaussian Errors
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Correlated errors: covariance
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Error propagation II: the general case
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Example continued
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Estimating the Correlation Coefficient
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Properties of the 2D Gaussian Distribution
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Properties of 2D Gaussian Distribution
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The Error Ellipse and Error Matrix
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General transformation of Errors
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A simple example
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A more involved example
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Summary
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Appendix: Error on Error - Justification
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