Statistics 100B: Introduction to Mathematical Statistics

Announcements

  • 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: 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.
  • 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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