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STAT410

STAT410 (Statistics and Probability II) is a 3 credit hour (4 graduate hour) statistics and probability course intended as a continuation of STAT400.

Content Covered

  • Moment generating functions
  • Joint probability distributions
  • Functions and transformations of random variables
  • Order statistics
  • Multivariate normal distribution
  • Gamma distribution
  • Point estimation
  • Estimators (MLE, MoM) and their properties (unbiasedness, consistency, efficiency)
  • Confidence intervals
  • Sufficient statistics
  • Hypothesis testing and power of tests

STAT410 assumes a solid understanding of the topics covered in STAT400. The course moves on to more advanced topics such as hypothesis testing and confidence intervals.

Prerequisites

STAT410 requires multivariable calculus knowledge, including double and triple integrals and partial derivatives. You will be expected to setup and calculate these integrals on the exam. It also requires a solid understanding of the topics covered in STAT400, since very little time is spent reviewing these topics.

When to Take It

This class is a replacement for ECE313 and allows you to take more advanced statistics and machine learning courses. It is best to take this class immediately after STAT400 since it builds directly on the topics covered in that class.

Course Structure

This class typically consists of 12 homework assignments, worth 10 points each. The lowest 2 homework assignments will be dropped. There are 2 midterm exams each worth 80 points, and a cumulative final exam worth 140 points.

The homework is quite challenging and will take a significant amount of time to complete. This is to prepare you for the exams, where problems are similar to the homework but have "nicer" numbers or reduced steps. The exams are fully written and you are allowed 1 double-sided note sheet as well as a calculator. The exams are written to take the full time, so you should be prepared to work quickly.

You should try to attend every lecture since they are not recorded and move quite quickly. Prof. Stepanov will post additional notes on Canvas, but they are not a substitute for attending lecture.

Instructors

Prof. Alexey Stepanov is typically the primary instructor for this course. Other sections may be taught by Prof. Yun Yang or Prof. Jeffrey Douglas.

Prof. Stepanov is an entertaining yet intense lecturer, and he expects you to be fully engaged during lecture. Due to this, he is a polarizing figure among students, with many finding him one of the best lecturers in the statistics department while others find him too intense. He hosts multiple office hours a week but expects you to be prepared with specific questions.

Course Tips

STAT410 is a rigorous statistics course, but it is generally considered easier than ECE313 since the STAT400 and STAT410 combination spreads out the topics over 2 semesters.

The homework is quite challenging and is designed to make you truly understand topics covered in lecture. You should start the homework early and seek help in office hours if you are stuck. The exams are much more straightforward than the homework, but you should still be prepared to work quickly. A calculator that is able to symbolically evaluate triple integrals (such as a TI-Nspire CX II CAS) is highly recommended for the exams.

Using the Piazza discussion board is a great way to get help on homework problems, both from other students and instructors.

DO NOT post homework problems or solutions on Chegg or Discord. The instructors are aware of this and will result in collective punishment for the entire class, such as a more difficult exam.

Prof. Stepanov has an odd sense of humor that is not for everyone, but he clearly wants his students to succeed. If you put in effort and attend office hours, he is incredibly knowledgeable and willing to help.

Life After

STAT410 is used to replace ECE313 so many machine learning/AI courses are available after taking STAT410. ECE majors pursuing a Statistics minor may opt for STAT410 instead of ECE313 to fulfill the minor requirements. STAT410 is also a prerequisite for many upper-level statistics courses, such as STAT425, STAT428, and STAT429.

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