MA280 Probability (Online)
Instructor
Information
Home Institution: Shanghai University of Finance and Economics
Term
June 26, 2023-July 21, 2023
Monday through Friday
Course Delivery
The class will be delivered in the format of online. Other than recorded
lecture videos, the instructor will arrange 4 hours’ real-time interactions
with students per week (via Zoom meeting, Tencent Meeting or Wechat).
Contact Hours
(Lecture Hours)
66 contact hours Credits 4 units
Self-study
13 extra hours per week * 4 weeks are required for independent reading and
research
Required Texts
(with ISBN)
A First Course in Probability, 10th Edition. S. Ross. Pearson
ISBN-13: 9780134753119.
Prerequisite N/A
2 / 5
Course Overview
This course introduces students to probability. Topics include probability spaces, conditional probability,
independence, univariate random variables, multivariate random variables, random vectors, expectation,
law of large numbers, central limit theorem.
Course Goals
A student who satisfactorily completes this course will be able to:
 understand the basic rules of probability, conditional probability and expectation;
 apply Bayes’ theorem on changing conditional probabilities with new evidence;
 understand the difference between discrete and continuous random variables;
 work easily with several common distributions, discrete and continuous;
 know what expectation and variance mean and be able to compute them;
 understand the central limit theorem.
Exams
Midterm Exam (30%): 2 hours’ Written Test
Final Exam (40%): 2 hours’ Written Test
3 / 5
Grading Policy
Type Description Weight
Homework Short answer questions 30%
Midterm
Examination
Written Test; On-line Submission 30%
Final Exam Written Test; On-line Submission 40%
Grading Scale is as follows
Number grade Letter grade GPA
90-100 A 4.0
85-89 A- 3.7
80-84 B+ 3.3
75-79 B 3.0
70-74 B- 2.7
67-69 C+ 2.3
65-66 C 2.0
62-64 C- 1.7
60-61 D 1.0
≤59 F (Failure) 0
4 / 5
Class Schedule
Date Lecture Readings Online Teaching Arrangement
Day 1 Combinatorial Analysis Chapter 1
Approximately 100 minutes’ pre-
recorded video lectures
Day 2
Axioms of probability,
Sample spaces having equally likely
outcomes
Chapter 2
Approximately 100 minutes’ pre-
recorded video lectures
Day 3 Conditional probability, Bayes formula Chapter 3
Approximately 100 minutes’ pre-
recorded video lectures
Day 4
Independent events, (⋅ |) is a
Probability
Chapter 3
Approximately 100 minutes’ pre-
recorded video lectures
Day 5 Discrete random variables Chapter 4
Approximately 100 minutes’ pre-
recorded video lectures plus 120
minutes’ online interaction via
Tencent Meeting and WeChat group
Day 6
Expectation and variance of discrete
random variables
Chapter 4
Approximately 100 minutes’ pre-
recorded video lectures
Day 7
Some important discrete probability
distributions
Chapter 4
Approximately 100 minutes’ pre-
recorded video lectures
Day 8
Continuous random variables,
Expectation and variance of continuous
random variables
Chapter 5
Approximately 100 minutes’ pre-
recorded video lectures
Day 9 Midterm Review
Approximately 100 minutes’ pre-
recorded video lectures plus 120
minutes’ online interaction via
Tencent Meeting and WeChat group
Day 10 Midterm Exam
Day 11
Some important continuous probability
distributions
Chapter 5
Approximately 100 minutes’ pre-
recorded video lectures
Day 12
The distribution of a function of a
random variable.
Chapter 5
Approximately 100 minutes’ pre-
recorded video lectures
Day 13
Jointly distributed random variables,
joint distribution functions,
independent random variables
Chapter 6
Approximately 100 minutes’ pre-
recorded video lectures
Day 14
Conditional distributions, Order
statistics, Joint probability distribution
of functions of random variables
Chapter 6
Approximately 100 minutes’ pre-
recorded video lectures
Day 15
Properties of expectation, Expectation
and variance of sums of random
variables, Covariance and correlations
Chapter 7
Approximately 100 minutes’ pre-
recorded video lectures plus 120
minutes’ online interaction via
Tencent Meeting and WeChat group
5 / 5
Day 16
Conditional expectation, Conditional
expectation and prediction,
Moment generating functions
Chapter 7
Approximately 100 minutes’ pre-
recorded video lectures
Day 17
Additional properties of normal
random variables,
General definition of expectation
Chapter 7
Approximately 100 minutes’ pre-
recorded video lectures
Day 18
Chebyshev’s inequality and the weak
law of large numbers,
Central limit theorem, Strong law of
large numbers
Chapter 8
Approximately 100 minutes’ pre-
recorded video lectures
Day 19 Final Review
Approximately 100 minutes’ pre-
recorded video lectures plus 120
minutes’ online interaction via
Tencent Meeting and WeChat group
Day 20 Final Exam On-line Submission