-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathindex.qmd
137 lines (100 loc) · 5.36 KB
/
index.qmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
## Overview {.unnumbered}
{fig-align="center"}
This book is adapted from *MAT921: Probability* at Southwest University
of Finance and Economics (RIEM). It is an introductory probability
course that aims to be not boring. In this course, we try to blend
**conventional teaching**, **interesting puzzles** and **data-oriented
practical skills**.
Course Instructor's email: [gamma12\@126.com](). Please indicate your
class and student ID when you email me.
## Syllabus
**Topic 1: Classical probabilities\
**How likely were some of your classmates born on the same day as you?
**Topic 2: Data and random variables**\
Why is your exam score in this class a random variable?
**Topic 3: Discrete distributions**\
How many earthquakes are likely to happen in a random year?
**Topic 4: Expectation and variance**\
How old are you expected to live?
**Topic 5: Continuous distributions**\
How long are you expected to wait in the queue at a restaurant?
**Topic 6: Limiting theorems**\
Why a lottery company never loses?
**Topic 7: Sampling distribution**\
How do I know I am taller than an average person?
## Assessment
**Quiz (20%).** There will be an arbitrary number of in-class quizzes.
The date for each quiz will be announced in advance. Each quiz will
consist of 1-2 questions based on material covered in previous weeks.
Suppose there are $n$ quizzes in total, only your top $n-1$ quiz scores
will count toward your final grade. This means you can miss or skip one
quiz without penalty.
**Project (20%).** The goal of this project is to encourage students to
apply the knowledge learned in this course to solve practical problems.
We will conduct a survey to gather information about the students in
this class. Using this data, you will carry out a mini research project,
in which you raise your own question and analyzing the data to answer it
(e.g. why some students perform better in exams than others). Essays
that present interesting questions and use the data persuasively to
support their conclusions will receive higher marks. Additionally,
selective students will be invited to present their findings to the
class.
**Final exam (60%).** The final exam will be a closed-book,
paper-and-pencil exam scheduled for Week 17. It will not simply repeat
lecture material but will assess your ability to apply the knowledge you
have gained to solve novel problems. To perform well, you must have a
deep understanding of the concepts and acquire some degree of
problem-solving skills. The average score of the past exam is 69 with a
standard deviation 15. The pass rate (\>=60) is about 80%.
{width="80%" fig-align="center"}
## Lecture notes
All lecture materials will be published through this online website. You
are not required to read any textbook. For students who insist on a
textbook, it would be:
- DeGroot and Schervish's *Probability and Statistics (4th edition).*
It is recommended to use the textbook as a supplement not a replacement of the
lecture note. For students who prefer to read the textbook. There are two key
differences between this lecture note and the textbook. First, the sections
are arranged differently. Second, the examples and exercises are entirely
different despite the key definitions and theorems are the same.
## Homework
There is no homework assignment in this course. We will do in-class
exercises instead. However, problem solving is essential for learning
math. You are encouraged to practice the exercises in DeGroot and
Schervish's textbook after class. But it is not mandatory.
## Statistical software
Statistical software is indispensable for modern statistics. For
practical consideration, it is beneficial to start learn it as early as
possible. We will demonstrate how to do statistics in R, which is a
widely-used open-source statistical programming language. It is highly
recommended that you try it yourself while learning this course, though
it is not mandatory.
## Students' evaluation
If you have not decided whether to enroll in this course or not. Here
are some surveys from the past students for your reference. In general,
this is not an easy course especially for freshmen. We will deal with
serious maths, though I will try to convey the beauty of the subject as
much as possible.
{fig-align="center"}
## Reference
1. Schervish, M. J., & DeGroot, M. H. (2014). *Probability and
statistics.* Pearson Education.
2. Blitzstein, J. K., & Hwang, J. (2019). *Introduction to
probability.* Chapman and Hall/CRC.
3. Hansen, B. (2022). *Probability and statistics for economists.*
Princeton University Press.
4. Grimmett, G., & Stirzaker, D. (2020). *Probability and random
processes.* Oxford University Press.
## Online playground
[Probability Playground: Interactive Probability
Distributions](https://www.acsu.buffalo.edu/~adamcunn/probability/probability.html)
[StatKey: Statistics Unlocking the Power of
Data](https://www.lock5stat.com/StatKey/index.html)
[MathIsFun: Standard Normal Distribution
Table](https://www.mathsisfun.com/data/standard-normal-distribution-table.html)
[Central Limit Theorem Demo](https://projects.oliverni.com/clt/)
## Copyright ©
The content on this website is made available for online viewing by the
public. Redistribution, reproduction, or any other use of the content,
in whole or in part, is prohibited without prior written permission from
the author.