College Mathematics 4 (Probability), Spring 2026

Lecturer:

  • Prof. Raphaël Ponge.
  • E-mail: ponge[dot]math[at]icloud[dot]com.
  • Office: Room 419 East, School of Mathematics (Wangjiang campus).
  • Office hours: By appointment.

Teaching Assistant:

  • Mr. Zhou, Kaijie
  • E-mail: zhoukaijie[at]stu[dot]scu[dot]edu[dot]cn.

Time and Location:

  • Lectures: Tuesdays from 08:15-09:55 in Room 201, Section 3, Liberal Arts Bldg. (Jiang’an campus).
  • Exercise Sessions: Fridays from 10:15-11:55 in Room 103, Block A, 1st Teaching Bldg. (Jiang’an campus).

Main Reference:

  • Probability and statistics for engineers and scientists by R. Walpole, R. Myers, S. Myers, and K. Ye, 9th Edition.

Grading Scheme:

  • 25% (Midterm exam), 25% (homework + attendance), 50% (Final Exam).
  • There will be at least 10 homework assignments.
  • The Midterm Exam will be on Saturday, May 9 (make-up day) from 08:15-09:55.
  • Date and time of Final Exam will be communicated later.

Slides of Lectures:

Chapter 2: Probability

  • Section 2.1: Sample space (slides).
  • Section 2.2: Events (slides).
  • Section 2.3: Counting sample points (slides).
  • Section 2.4: Probability of an event (slides).
  • Section 2.5: Additive Rules (slides).
  • Section 2.6: Conditional probability, independence, and the Product Rule (slides).
  • Section 2.7: Bayes’ Rule (slides).

Chapter 3: Random Variables and Probability Distributions

  • Section 3.1: Concept of a random variable (slides).
  • Section 3.2: Discrete probability distributions (slides).
  • Section 3.3: Continuous probability distributions (slides).
  • Section 3.4: Joint probability distributions (slides).

Chapter 4: Mathematical Expectation

  • Section 4.1: Mean of a random variable (slides).
  • Section 4.2: Variance and covariance of random variables (slides; whole material).
  • Section 4.3: Means and Variances of linear combinations of random variables (slides).

Homework Assignment:

Homework 1 (due April 3):

  • Section 2.2: # 4, 8, 14.
  • Section 2.3: # 22, 32, 38, 46.
  • Section 2.5: # 50, 56, 62.

Homework 2 (due April 10):

  • Section 2.6: # 74, 76, 82.
  • Section 2.7: # 96, 98, 102.
  • Section 3.3: # 2, 4, 12.

Homework 3 (due April 17):

  • Section 3.3: # 3.6, 3.8, 3.14, 3.18, 3.20, 3.22.

Homework 4 (due April 24):

  • Section 3.4: # 3.38, 3.42, 3.50, 3.52, 3.56, 3.60.

Homework 5 (due May 8):

  • Section 4.1: # 4.4, 4.10, 4.14, 4.26.
  • Section 4.2: # 4.34, 4.40, 4.50, 4.52.