# Statistics 100B: Introduction to Mathematical Statistics

### Announcements

• First lecture is on Tuesday, 03 August 2021
Location: Online - Recorded
Day/time: TR 09:00 - 10:50
See you then!

• http://www.socr.ucla.edu

#### • http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials

### Handouts

• 1. Summary of discrete and continuous distributions (review from Statistics 100A).
• The next five links are the statistical tables needed for the entire quarter (from "Mathematical Statistics and Data Analysis", by John Rice, Doxbury Press, Second Edition (1995)).
Table 1: Standard normal distribution table (Z).
Table 2: Chi-square distribution table.
Table 3: t distribution table.
Table 4: F distribution table (95th percentiles).
Table 5: F distribution table (99th percentiles).
• 2. Some review material from Statistics 100A.
• 3. Simulation of random variables.
• 4. Covariance and correlation.
• 5. Poisson, Exponential, and Gamma distributions.
• 6. Exponential families and properties.
• 7. Moment generating functions and properties.
• 8. Beta distribution.
• 9. Central limit theorem: proof and examples.
• 10. Joint moment generating functions and properties.
• 11. Functions of random variables and joint distributions of functions of random variables.
• 12. Multivariate normal distribution.
• 13. Distributions related to normal (chi square, t, F).
• 14. The F distribution probability density function.
• 15. Noncentral chi square distribution.
• 16. Noncentral chi square, t, and F distributions in R.
• 17. Properties of estimators - Information, Cramer-Rao inequality.
• 18. R commands for MSE (three different estimators for p).
• 19. See R commands of handout #18.
• 20. Method of maximum likelihood.
• 21. Order statistics.
• 22. Order statistics - derivations.
• 23. Order statistics - a simulation example.
• 24. Method of moments.
• 25. Sufficiency.
• 26. Confidence intervals.
• 27. Bootstrap confidence intervals.
• 28. Hypothesis testing I.
• 29. "Statistics in the courtroom", by George Cobb and Stephen Gehlbach.
• 30. Hypothesis testing II.
• 31. Paired t test.
• 32. Article related to the paired t test.
• 33. Analysis of variance (ANOVA).
• 34. ANOVA - F test.

### Practice problems

• Practice 1.
• Practice 1 - solutions.
• Practice 2.
• Practice 2 - solutions.
• Practice week 3.
• Practice week 3 - solutions.
• Multivariate normal practice problems.
• Multivariate normal practice problems solutions.
• Practice final exam.
• Practice final exam - solutions.

### Quizzes

• Quiz 1.
• Quiz 1 - solutions.
• Quiz 2.
• Quiz 2 - solutions.

### Homework

• Homework 1. Due by 22:00 on Friday, 08/06.
• Homework 1 - solutions.
• Homework 2. Due by 22:00 on Monday, 08/09.
• Homework 2 - solutions.
• Homework 3. Due by 22:00 on Saturday, 08/14.
• Homework 3 - solutions.
• Homework 4. Due by 22:00 on Tuesday, 08/17.
• Homework 4 - solutions.
• Homework 5. Due by 22:00 on Sunday, 08/22.
• Homework 5 - solutions.
• Homework 6. Due by 22:00 on Sunday, 08/29.
• Homework 6 - solutions.
• Homework 7. Due by 22:00 on Tuesday, 08/31.
• Homework 7 - solutions.
• Homework 8. Due by 22:00 on Saturday, 09/04.
• Homework 8 - solutions.
• Homework 9. Due by 22:00 on Tuesday, 09/07.
• Homework 9 - solutions.
• Homework 10. Due by 22:00 on Thursday, 09/09.