Statistics 100B: Introduction to Mathematical Statistics

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  • For the course syllabus click here.

    Useful links:

  • http://www.socr.ucla.edu

    It's online, therefore it exists!


  • 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. Moment generating functions and properties.
  • 7. Joint moment generating functions and properties.
  • 8. Practice questions on gamma distribution.
  • 9. Multivariate normal distribution.
  • 10. Central limit theorem: proof and examples.
  • 11. Distributions related to normal (chi square, t, F).
  • 12. Exam 1 - practice exam I.
  • 13. Exam 1 - practice exam II.
  • 14. Exam 1 - practice exam III.
  • 12a. Exam 1 - practice exam I - solutions.
  • 13a. Exam 1 - practice exam II - solutions.
  • 14a. Exam 1 - practice exam III - solutions.
  • 15. Fall 2016 exam 1.
  • 15a. Fall 2016 exam 1 - solutions.
  • 16. Properties of estimators - Fisher information, Cramer-Rao inequality.
  • 17. R commands for MSE (three different estimators for p).
  • 18. See R commnds of handout #17.
  • 19. Method of maximum likelihood.
  • 20. Order statistics.
  • 21. Method of moments.
  • 22. Simple regression analysis.
  • 23. Midterm 1 solutions.
  • 24. Practice exam for midterm 2.
  • 25. Practice exam for midterm 2 - solutions.
  • 26. Confidence intervals.
  • 27. Bootstrap confidence intervals.

    Practice problems

  • Practice 1.
  • Practice 1 - solutions.
  • Practice 2.
  • Practice 2 - solutions.
  • Practice 3.
  • Practice 3 - solutions.
  • Practice 4.
  • Practice 4 - solutions.
  • Practice 5.
  • Practice 5 - solutions.

    Homework

  • Homework 1. Due by 22:00 on Friday, 01/12.
  • Homework 1 - solutions.
  • Homework 2. Due by 22:00 on Wednesday, 01/17.
  • Homework 2 - solutions.
  • Homework 3. Due by 22:00 on Friday, 01/19.
  • Homework 3 - solutions.
  • Homework 4. Due by 22:00 on Thursday, 01/25.
  • Homework 4 - solutions.
  • Homework 5. Due by 22:00 on Tuesday, 01/30.
  • Homework 5 - solutions.
  • Homework 6. Due by 22:00 on Wednesday, 02/07.
  • Homework 6 - solutions.
  • Homework 7. Due by 22:00 on Tuesday, 02/13.
  • Homework 7 - solutions.
  • Homework 8. Due by 22:00 on Tuesday, 02/20.
  • Homework 8 - solutions.

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