Statistics 100B: Introduction to Mathematical Statistics
Announcements

First lecture is on Monday, 04 January 2021
Location: Online  Recorded
Day/time: MWF 13:00  13:50
See you then!
For the course syllabus click
here.
Useful links:
http://www.socr.ucla.edu
http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials
Download R and packages.
Download RStudio.
Labs
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: Chisquare 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, CramerRao 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.
Practice week 4  I.
Practice week 4  I solutions.
Practice week 4  II.
Practice week 4  II solutions.
Multivariate normal practice problems.
Multivariate normal practice
problems solutions.
Practice week 7  A.
Practice week 7  A solutions.
Practice week 7  B.
Practice week 7  B solutions.
Practice week 7  C.
Practice week 7  C solutions.
Practice week 7  D.
Practice week 7  D solutions.
Practice final exam.
Practice
final exam  solutions.
Homework
Homework 1. Due
by 22:00 on Tuesday, 01/12.
Homework 1  solutions.
Homework 2. Due
by 22:00 on Thursday, 01/21.
Homework 2  solutions.
Homework 3. Due
by 22:00 on Monday, 01/25.
Homework 3  solutions.
Homework 4. Due
by 22:00 on Tuesday, 02/02.
Homework 4  solutions.
Homework 5. Due
by 22:00 on Sunday, 02/07.
Homework 5  solutions.
Homework 6. Due
by 22:00 on Tuesday, 02/16.
Homework 6  solutions.
Homework 7. Due
by 22:00 on Tuesday, 02/23.
Homework 7  solutions.
Homework 8. Due
by 22:00 on Tuesday, 03/02.
Homework 8  solutions.
Homework 9. Due
by 22:00 on Tuesday, 03/09.
Homework 9  solutions.
Homework 10. Due
by 22:00 on Saturday, 03/13.
Homework 10  solutions.
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Home page.