Applied Mathematics 1650

Statistical Inference I

Brown University, Summer 2016

Mon, Tue, Wed, Thu 1-3 pm

Kassar House 105

APMA 1650 is an integrated first course in mathematical statistics. The first half of the course covers probability, and the last half is statistics, integrated with its probabilistic foundation. Specific topics include probability spaces, discrete and continuous random variables, methods for parameter estimation, confidence intervals, and hypothesis testing.


Instructor: Ross Parker (

TA: James Zhang (

Office Hours:

  • Mon 12-1 pm (Ross), Kassar House 105
  • Tue 3-4 pm (James), Kassar House 105
  • Wed 3-4 pm (Ross), Kassar House 105
  • Thu 12-1 pm (James), Kassar House 105

Recitation Section: Wed 12-1 pm, Kassar House 105

Prerequisites: One year of university-level calculus. At Brown, this corresponds to MATH 0100, MATH 0170, or MATH 0180. A score of 4 or 5 on the AP Calculus BC exam is also sufficient. Multivariable calculus (MATH 0190, MATH 0200, or MATH 0350 at Brown) will be helpful for one small part of the course, but is not required. I will teach any multivariable techniques we use in detail.

Class format: This course will combine lectures and small-group discussions. We will meet for two hours four times per week. There will be a five-minute break at the halfway point. There will also be an optional one-hour recitation session during which students will work on problems in groups. Problems in recitation section make great practice for the exams! There will be two midterm exams (July 13 and July 28) and one final exam (Thursday, August 11). I will hold review sessions prior to each exam.

Homework: There will be eight problem sets total, which is approximately two per week. Problem sets will be due on Mondays and Thursdays (with the exception of the week of July 4; due to the federal holiday, problem sets will be due on Tuesday and Thursday that week). On weeks when there is an exam, there will be no problem set due on Thursday. There are no problem sets due the first week of class. Problem sets will be posted at least one week in advance of the due date. Homeworks may be submitted in class on the due date, or they may be dropped in the APMA 1650 homework box in 182 George St. by 3:45 pm on the due date. (182 George St. closes at 4 pm during the summer, hence the 3:45 deadline for submission). You are encouraged to work together on assignments, but you must write up your own solutions.

Homework policy: Late assignments generally will not be accepted. That being said, I understand that the unexpected does happen. If you have a serious situation in which you will believe you will be unable to complete your assignment on time, please contact me directly and we will arrange something.

Textbooks: Lectures will be based on my own notes, which will be posted on this website after each class. Due to the prohibitive cost of textbooks (approximately $290 for the traditionally required textbook), I cannot with good conscience ask you to purchase a textbook for this class. That being said, a textbook is a valuable reference, both to clarify points made in class and as a source of practice problems. I will place multiple copies of the following textbook on reserve in the Rockefeller Library.

  • Wackerly, Mendenhall, and Scheaffer, Mathematical Statistics with Applications, 7th Edition. Thomson Brooks/Cole, 2008. This has been the required textbook in the past for APMA 1650. If you wish to have your own physical copy, the 6th edition (2001) is not significantly different and can usually be found used on for less than $20.

Grade Distribution:

  • Problem sets: 30%
  • Midterm exam 1: 20%
  • Midterm exam 2: 20%
  • Final exam: 30%


Week 1 (June 27 - 30): Introduction to Probability

  • June 27: Introduction, probability spaces
  • June 28: Counting: permutations, combinations, and multinomials, oh my!
  • June 29: Conditional probability and Bayes's rule
  • June 30: Expected values and variance

Week 2 (July 4 - 7): Random Variables

  • July 4: Independence Day holiday, no class!
  • July 5: Discrete random variables
  • July 6: Continuous random variables
  • July 7: Continuous random variables
  • July 8: Review session for Midterm 1, 11-1 pm in Wilson 205

Week 3 (July 11 - 14): Multivariate Distributions

  • July 11: Multivariate distributions, review of calculus in two dimensions
  • July 12: Multivariate distributions (will be taught by a guest instructor)
  • July 13: Midterm exam 1 (covers material up to discrete random variables)
  • July 14: No class!

Week 4 (July 18 - 21): Sampling and Estimators

  • July 18: Multivariate distributions, covariance, correlation
  • July 19: Sampling, estimators, bias, MSE
  • July 20: Central limit theorem, error of estimation, confidence intervals
  • July 21: Methods of Moments, MLE

Week 5 (July 25 - 28): Hypothesis Testing

  • July 25: Hypothesis testing, review session for Midterm 2 after class
  • July 26: Hypothesis testing
  • July 27: Hypothesis testing
  • July 28: Midterm exam 2 (covers material up to bias and MSE of estimators)

Week 6 (Aug 1 - 4): Likelihood Ratio Tests and Linear Regression

  • Aug 1: Likelihood ratio tests
  • Aug 2: Computing samples and Monte Carlo methods
  • Aug 3: Linear regression
  • Aug 4: Bayesian Inference

Week 7 (Aug 8 - 11): Review and Final Exam

  • Aug 9: Review session for final exam, 1-3 pm in Barus and Holley 155
  • Aug 11: Final exam. Kassar House 105, 1-4 pm