36-625 Probability and Mathematical Statistics I



ANNOUNCEMENTS:

Test 3 is Friday


Practice test 3: PRACTICE TEST 3


Instructor: Larry Wasserman
Class Time: MWF 2:30-3:20
Place: Porter Hall A18C

Office Hour: Monday 1:00 - 2:00 Baker Hall 228a
TA: Kristina Klinkner
TA Office hours: Wed 5-6 and Thurs 12-1
Place: FMS 320

Course secretary: Mari-Alice McShane
Office: Baker Hall Baker Hall 229K

Course description

This is an intense, fast-paced course on probability and statistics. It is intended for undergraduates in Statistics, Mathematics and Computer Science and also for graduate students in Computer Science and related fields. I assume you have a strong background in calculus and a knowledge of basic linear algebra (vectors and matrices). The course is excellent preparation for studying statistics, machine learning, data mining and artificial intelligence. I do not assume any knowledge of probability or statistics but be forewarned that the course does move rapidly.

Prerequisites

Calculus and linear algebra.

The syllabus includes information about assignments, exams and grading.

Text: All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman (2004).

Other References
Elementary: Probability and Statistics Third Edition by Morris H. DeGroot and Mark J. Schervish (2002). Addison-Wesley.
Intermediate: Statistical Inference George Casella and Roger Berger (1990). Wadsworth.
Advanced: Theory of Point Estimation. Eric Lehmann and George Casella (1998). Springer.
Very Advanced: Asymptotic Statistics. Aad van der Vaart (1998). Cambridge.

Assignments

Assignments are due on Thursdays at 3:00 p.m. Hand in the assignment to Mari-Alice McShane Baker Hall 229K.
  • Assignment 2: due: Thursday, September 18 by 3:00
  • Assignment 3: due: Thursday, October 2 by 3:00
  • Assignment 4: due: Thursday, October 16 by 3:00
  • Assignment 5: due: Thursday, October 30 by 3:00
  • Assignment 6: due: Thursday, November 13 by 3:00
  • Assignment 7: due: TUESDAY November 25 by 3:00

    SOLUTIONS
  • Solutions to Assignment 2
  • Solutions to Assignment 3
  • Solutions to Assignment 4
  • Solutions to Test 1
  • Solutions to Test 2
  • Solutions to Assignment 5
  • Solutions to Assignment 6
  • R code Assignment 6
  • plot for Assignment 6 q. 7 (normal)
  • plot for Assignment 6 q. 7 (Cauchy)
  • Solutions to Assignment 7

    The R language and code

    Data

    Topics

    • Introduction to Probability
    • Random Variables
    • Expectation and Variance
    • Inequalities
    • Convergence of Random Variables
    • Statistical Models
    • Point Estimation
    • Confidence Intervals
    • Testing

    Course Calendar
    Week of:   Mon Tues Wed Thursday Friday
    August 25 Probability   Probability   Random Variables
    September 1 No Class (Labor Day)   Discrete and Continuous Random Variables Homework 1 Bivariate Distributions
    September 8 Conditional Distributions/ Multivariate Distributions   Transformations   Expected Values
    September 15 Expectation and Variance   Review Homework 2 Test 1
    September 22 Covariance and Moment generating functions   Inequalities   Inequalities
    September 29 Convergence   Convergence Homework 3 Convergence
    October 6 Delta method   VC theory   Inference
    October 13 Bias and Variance, Bootstrap   Bootstrap Homework 4 MIDSEMESTER BREAK
    October 20 Bootstrap   Review   Test 2
    October 27 Parametric Inference   Maximum Likelihood Homework 5 Maximum Likelihood
    November 3 Maximum likelihood   Multiparameter MLE   Sufficiency/ Exponential Families
    November 10 Hypothesis Testing   Hypothesis Testing Homework 6 Hypothesis Testing
    November 17 Hypothesis Testing   Bayesian Inference   Bayesian Inference
    November 24 Bayesian Inference Homework 7 NO CLASS   NO CLASS
    December 1 Review   Review   Test 3