NTRODUCTION TO PROBABILITY AND STATISTICS

Class Number: 3317

Delivery Method: In Person

Overview

• COURSE TIMES + LOCATION:Mo, We, Fr 9:30 AM – 10:20 AM
  REMOTE LEARNING, Burnaby
• EXAM TIMES + LOCATION:Apr 28, 2021
  12:00 PM – 3:00 PM
  REMOTE LEARNING, Burnaby
• INSTRUCTOR:Derek Bingham
  [email protected]
• PREREQUISITES:or Corequisite: MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first.

Description

CALENDAR DESCRIPTION:

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Quantitative.

COURSE DETAILS:

STAT Workshop Coordinator: Harsha PereraOutline:

1. Introduction to graphical and numerical descriptive statistics including the histogram, boxplot, scatterplot, sample mean, sample median, sample standard deviation, sample coefficient of relative variation, and sample correlation coefficient.
2. Elementary probability rules, basic combinatorial formulae, conditional probability, Bayes’ Theorem, and independence.
3. Introduction to discrete distributions including the probability mass functions, expectation, the binomial distribution, and the Poisson distribution.
4. Introduction to continuous distributions including the probability density function, expectation, variance, coefficient of variation, the cumulative distribution function, uniform distribution, gamma distribution, exponential distribution, normal distribution, normal approximation to the binomial distribution, jointly distributed random variables, statistics and their distributions, the Central Limit Theorem.
5. Single sample inference including estimation and testing of proportions and means.
6. Two sample inference including estimation and testing of differences in proportions and differences in means (paired and non-paired data).

Mode of teaching:

Lecture: synchronous (recorded)
Stats Workshop/tutorial: asynchronous
Quizzes: synchronous; dates TBA
Final exam: synchronous; date TBA

Remote invigilation with Zoom will be used for the final exam and so access to high-speed internet with audio and webcam will be required. During invigilation, camera and audio must be on with a full view of the workspace.This course is accredited under the Canadian Institute of Actuaries (CIA) University Accreditation Program (UAP). Achievement of the minimum required grades in accredited courses may provide credit for preliminary exams. Please note that a combination of courses may be required to achieve exam credit. Details on the required courses and grades for the Simon Fraser University can be found here.

In addition to the specific university’s internal policies on conduct, including academic misconduct, candidates pursuing credits for writing professional examinations shall also be subject to the Code of Conduct and Ethics for Candidates in the CIA Education System and the associated Policy on Conduct and Ethics for Candidates in the CIA Education System. For more information, please visit information for candidates on obtaining UAP credits.

COURSE-LEVEL EDUCATIONAL GOALS:

Grading

• Quizzes (best 5 out of 6) 65%
• Final Exam 35%

NOTES:

• There will be no make-up quizzes.
• You must pass the final exam in order to pass the course.
• Students should be aware that the exam will be invigilated remotely and that they will be asked to show their work area to invigilators at all times.

Above grading is subject to change.

Materials

MATERIALS + SUPPLIES:

Access to high-speed internet, webcam

REQUIRED READING:

Required Textbook:Introduction to Probability and Statistics, 2nd ed. by Tim Swartz. Publisher: Pearson.
ISBN: 978-1-269-73721-0

DEPARTMENT UNDERGRADUATE NOTES:

Students with Disabilities:
Students requiring accommodations as a result of disability must contact the Centre for Accessible Learning 778-782-3112 or [email protected]
Tutor Requests:
Students looking for a Tutor should visit http://www.stat.sfu.ca/teaching/need-a-tutor-.html. We accept no responsibility for the consequences of any actions taken related to tutors.

REGISTRAR NOTES:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN SPRING 2021

Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning ([email protected] or 778-782-3112).

Question 1: Consider a random variable $X$, with the following probabllity density function. Flnd $E(X)$.
$f(x)=\left{\begin{array}{ll}
1 / 2 & 0<z<1 \
1 / 2+c(x-1) & 1 \leq z<3
\end{array}\right.$

Question 2: If $E(X)=3$ and $V \operatorname{ar}(X)=4 .$ Find
(a) $E\left[(X+3)^{2}\right]$
(b) $\operatorname{Var}(2+4 X)$

Question 3: Consider two random variables $X$ and $Y$ taat are independent froen each other and only take on values $-1,0,$ and 2. We have:
$P(X=-1)=P(X=2)=1 / 3$
$P(Y=-1)=P(Y=0)=1 / 4$
If $Z=5 X+4 Y+2 .$ Find $E(Z)$ and $V \operatorname{ar}(Z)$.

Question 4: Consider $f(x, y)=\frac{6}{7}\left(x^{2}+\frac{x y}{2}\right), 01 \mid X=1)$

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