Spring 2027

Introduction to Probability and Mathematical Statistics I

Introduction to Probability and Mathematical Statistics I covers probability theory, combinatorial methods, discrete and continuous distributions, moments, and estimation.

offering recorded3 credits
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 6

Past student reviews · Garvesh Raskutti

One student found exams crazy difficult and felt the instructor assumed students had taken analysis. Another said open-book exams required high mathematical skills.

What you’ll be able to do

  • Recall the definitions of fundamental objects and concepts underlying probability theory (e.g. sample spaces and events, the axioms of probability, the notions of conditional probability and independence, random variables and their probability distributions, mathematical expectation, and the joint distribution of one or more random variables) and demonstrate understanding of their properties

  • Perform important operations in probability (e.g. calculate the probabilities of events, derive the probability distributions of random variables, compute moments and the expectation of functions of random variables, calculate covariances and correlations, and obtain conditional distributions and conditional expectations) and interpret the results

  • Explain the meaning of key results in probability theory that are especially important in mathematical statistics (e.g. Bayes’ Theorem, probabilistic tail inequalities such as Markov’s and Chebyshev’s inequalities, the Law of Large Numbers, and the Central Limit Theorem)

  • Identify, utilize, and understand the key properties of, probability distributions that are especially important in statistics, including discrete families of distributions (e.g. the binomial, Poisson, geometric, and negative binomial distributions) and continuous families of distributions (e.g. the uniform, exponential, gamma, and normal distributions)

Source: UW Guide 1 UW Guide 2

Grade history

↗
average GPA
letter grades
A
AB
B
BC
C
D
F

All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 234, 376, or concurrent enrollment. Not open to students with credit forSTAT/​MATH 431 or STAT 311

MATH/STAT 309 used by

“Used by” includes alternatives; linked courses may have other requirements. This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

ANRU ZHANG is recorded teaching in Fall 2015, Fall 2016, Spring 2017, Spring 2018, Fall 2018, Spring 2019. Recorded history may be incomplete and does not establish a future schedule.

BRET LARGET is recorded teaching in Fall 2008, Fall 2009. Recorded history may be incomplete and does not establish a future schedule.

GARVESH RASKUTTI is recorded teaching in Fall 2013, Spring 2014, Fall 2014, Fall 2015, Spring 2016, Fall 2016, Spring 2017, Fall 2017, Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

KRISHNAKUMAR BALASUBRAMANIAN is recorded teaching in Spring 2015, Spring 2016. Recorded history may be incomplete and does not establish a future schedule.

MATTHEW BLOSS is recorded teaching in Spring 2025, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

NIMAL WICKREMASINGHE is recorded teaching in Spring 2023. Recorded history may be incomplete and does not establish a future schedule.

PANDUAN AN is recorded teaching in Fall 2019, Spring 2020, Fall 2020, Fall 2022, Spring 2024, Fall 2024, Fall 2025, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

RISHABH DUDEJA is recorded teaching in Fall 2023, Fall 2024, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

YAZHEN WANG is recorded teaching in Fall 2010, Fall 2011, Fall 2012. Recorded history may be incomplete and does not establish a future schedule.

Recorded history may be incomplete and does not establish a future schedule.

Calendar & sections

Spring 2027

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist
LEC 001Classroom Instruction0 / 660
DIS 311Classroom Instruction0 / 220
DIS 312Classroom Instruction0 / 220
DIS 313Classroom Instruction0 / 220
LEC 002Classroom Instruction0 / 660
DIS 321Classroom Instruction0 / 220
DIS 322Classroom Instruction0 / 220
DIS 323Classroom Instruction0 / 220
LEC 001Classroom Instruction0 / 660
DIS 311Classroom Instruction0 / 220
DIS 312Classroom Instruction0 / 220
DIS 313Classroom Instruction0 / 220
LEC 002Classroom Instruction0 / 660
DIS 321Classroom Instruction0 / 220
DIS 322Classroom Instruction0 / 220
DIS 323Classroom Instruction0 / 220

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections. Enrollment reflects scan time.

Meeting source records
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Student experience

the class

Past student reviews · Rishabh Dudeja, Matthew Bloss

One student found Rishabh Dudeja's lectures clear and well-structured, while another found Matthew Bloss's lectures decent but annoying due to a textbook change.

Recent recorded grades — Spring 2025: 3.45 GPA, 59.4% A/AB (n=69 letter grades); Fall 2025: 3.33 GPA, 64.2% A/AB (n=137 letter grades); Spring 2026: 2.98 GPA, 47.5% A/AB (n=120 letter grades).

difficulty & workload

Past student reviews · Garvesh Raskutti

One student found exams crazy difficult and felt the instructor assumed students had taken analysis. Another said open-book exams required high mathematical skills.

Past student reviews · Panduan An, Yazhen Wang

One student found lectures pointless because the professor wrote textbook problems with little explanation. Another found the required textbook was never used and said not to buy it.

Topics

  • Probability theory and combinatorial methods
  • Discrete and continuous, univariate and multivariate distributions
  • Expected values, moments, normal distribution, derived distributions, and estimation

Skills

  • Calculate probabilities, derive distributions, compute moments and expectations, and perform statistical estimation using probability theory.

Grades

Historical instructor

Spring 2027 · Projected

Before grades are released

– average GPA

Approximate 80% prediction interval

About this estimate

The course’s semester-average GPA, not an individual student’s grade. The center uses 5 same-season terms, weighted toward recent results.

The range uses the finite-sample 80th-percentile rank of absolute errors from earlier same-season forecasts. Each forecast uses only records from earlier terms. At least four forecasts are required; bounds are rounded outward and limited to 0–4. This is an empirical estimate: changing instructors or grading policies can reduce its coverage.

8 earlier forecasts · 0.33 GPA average error.

Grades over time

Through Spring 2027

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Spring 2026 · all course levels

GPA

Higher than % of other courses in this group.

Course GPAs · red marks this course’s range

letter grades

More recorded grades than % of other courses in this group.

Typical course in this group: letter grades.

About this comparison

1280 courses over the same term, each with at least 30 recorded letter grades. Cross-listed courses count once. GPA is not a measure of difficulty or teaching quality. The typical course is the median by recorded grade count; tied values are not counted as lower. Grade counts describe course scale, not unique students or typical section size.

Descriptions compare GPA with this group’s average: at least 0.20 higher or lower; otherwise close to average. Section size uses median recorded enrollment: small up to 30, mid-sized 31–99, large 100+. Lectures and discussion/lab sections are described separately.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

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Selected offering source records
MATH/STAT 309 · Spring 2027

Introduction to Probability and Mathematical Statistics I

Recorded 2026-10-14
MATH/STAT 309 · Spring 2027

Introduction to Probability and Mathematical Statistics I

Recorded 2026-10-14
Raw records 
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Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

Explore recorded grades
Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
Download part 1
Full model traces

Recorded model configuration, reasoning, and tool conversations.

Download part 1Download part 2
Model & dataset provenance 
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  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
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  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
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}