12 CONTENTS
38.8 Moment Generating Functions . . . . . . . . . . . . . . . . . . . . . . . . 78738.9 Independence and Conditional Probability . . . . . . . . . . . . . . . . . . 791
39 Statistical Tests 79739.1 The Distribution of nS2/σ2 . . . . . . . . . . . . . . . . . . . . . . . . . . 798
39.1.1 Confidence Intervals for Variance . . . . . . . . . . . . . . . . . . 80239.2 The T and F Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 805
39.2.1 The T Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 80539.2.2 Confidence Intervals for the Mean . . . . . . . . . . . . . . . . . . 80739.2.3 Testing For Two Different Means . . . . . . . . . . . . . . . . . . 81039.2.4 The F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 81239.2.5 Confidence Intervals for the Ratio of Two Variances . . . . . . . . 814
39.3 Maximum Likelihood Estimates . . . . . . . . . . . . . . . . . . . . . . . 81639.4 Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81839.5 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82539.6 Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83239.7 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839
A The Theory Of The Riemannn Integral∗ 843A.1 An Important Warning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843A.2 Basic Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843A.3 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846A.4 Which Functions Are Integrable? . . . . . . . . . . . . . . . . . . . . . . . 849A.5 Iterated Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857A.6 The Change Of Variables Formula . . . . . . . . . . . . . . . . . . . . . . 861A.7 Some Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869
B A Rigid Body Rotating About a Point 871
C Lagrangian Mechanics 877C.1 The Spinning Top and the Euler Angles . . . . . . . . . . . . . . . . . . . 880Copyright © 2018, You are welcome to use this, including copying it for use in classes
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