Lectures on Statistics

Contents:

1. Transformation of Random Variables

2. Jacobians

3. Moment-generating functions

4. Sampling from a normal population

5. The T and F distributions

6. Order statistics

7. The weak law of large numbers

8. The central limit theorem

9. Estimation

10. Confidence intervals

11. More confidence intervals

12. Hypothesis testing

13. Chi square tests

14. Sufficient statistics

15. Rao-Blackwell theorem

16. Lehmann-Scheff ́e theorem

17. Complete sufficient statistics for the exponential class

18. Bayes estimates

19. Linear algebra review

20. Correlation

21. The multivariate normal distribution

22. The bivariate normal distribution

23. Cram ́er-Rao inequality

24. Nonparametric statistics

25. The Wilcoxon test.

 Preface and Table of Contents
Lectures 1-5
Lectures 6-10
Lectures 11-15
Lectures 16-20
Lectures 21-25
Solutions to Problems
Index

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