# Lectures on Statistics (Robert Ash, University of Illinois at Urbana)

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About *Lectures on Statistics (Robert Ash, University of Illinois at Urbana):*

Excerpts from notes:

These notes are based on a course that I gave at UIUC in 1996 and again in 1997. No prior knowledge of statistics is assumed. A standard first course in probability is a prerequisite, but the first 8 lectures review results frombasic probability that are important in statistics. Some exposure to matrix algebra is needed to cope with the multivariate normal distribution in Lecture 21, and there is a linear algebra review in Lecture 19. Here are the lecture titles:

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

These notes are based on a course that I gave at UIUC in 1996 and again in 1997. No prior knowledge of statistics is assumed. A standard first course in probability is a prerequisite, but the first 8 lectures review results frombasic probability that are important in statistics. Some exposure to matrix algebra is needed to cope with the multivariate normal distribution in Lecture 21, and there is a linear algebra review in Lecture 19. Here are the lecture titles:

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