MEDIPOL - 2149080
Probability and Random Variables
Fall 2021-22
Oct. 8th, 2021
Assist. Prof. Hasan Kurt
hasankurt@medipol.edu.tr
About the Course
• One of the fundamental classes of engineering
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EEE – Communications, Random analysis
CoE – Algorithm Analysis, M. Learning, Decision Making
BME – Statistics, Modelling
IE – Stochastic, Modelling, Decision Making
CEE – Modelling in different fields, climate modelling
• Do not fail this course.
• Starts with very simple topics
– Then gets heavier, heavier, heavier, ….
• Heavy in workload.
• You will need enjoy the class once you
realize what is it for.
Class Pre-requisites
http://sens.medipol.edu.tr/undergraduate-programs/
Course Goals
• This is a second-year undergraduate course on
introduction to probability and random variables.
• This course will
– introduce fundamental differences between statistics and
probability
– introduce basic topics of probability.
– deliver probability axioms, probability density functions,
joint pdfs, and random variables with related topics are
covered throughout the course.
– deliver the importance of mathematical models for
analysis and synthesis
– Ability to exploit probabilistic approaches for real world
problems.
– Transformations of random variables
– have heavy usage of computer simulations so that the
theory in class is verified via simulations.
Course Content
WEEK
TOPIC
REFERENCE
Week 1
Class Info, Introduction to Statistics and Probability
Syllabus, Text 1-Chap. 1, Text 2-Chap. 1 &2
Week 2
Probability
Text 1-Chap. 2, Text 2-Chap 3
Week 3
Conditional Probability
Text 1-Chap. 2, Text 2-Chap 4
Week 4
Discrete Random Variables and their statistics
Text 1-Chap. 3, Text 2-Chap 5
Week 5
Discrete distributions and their statistics.
Text 1-Chap. 3, Text 2-Chap 6
Week 6
Continuous Random Variables and their statistics
Text 1-Chap. 4, Text 2-Chap 10
Week 7
Continuous Random Variables (Cont.)
Text 1-Chap. 4, Text 2-Chap 10
Week 8
Exam Week
All Lecture still Week 8
Week 9
Continuous Distributions
Text 1-Chap. 4, Text 2-Chap 11
Week 10
Multiple Discrete Random Variables
Text 1-Chap. 5, Text 2-Chap 7
Week 11
Multiple Continuous Random Variables
Text 1-Chap. 5, Text 2-Chap 12
Week 12
Conditional Probability Mass Functions
Text 1-Chap. 5, Text 2-Chap 8
Week 13
Conditional Probability Density Functions
Text 1-Chap. 5, Text 2-Chap 13
Week 14
Conditional Probability Density Functions
Text 1-Chap. 5, Text 2-Chap 13
Learning Outcomes
Students who successfully complete the course have reliably
demonstrated the ability:
– Model simple probabilistic phenomena mathematically.
– Calculate probabilities of events in a known event space,
expected values, variances of random variables, and conditional
probability
– The use of mathematical tools for discrete and continuous
random variables
– The ability to understand the common probability distributions
and the understanding of where to use them. The ability to
derive the statistics and other functions of the distribution.
– Ability to work with multiple random variables, their joint
distributions, their conditional distributions, and their onedimensional and two-dimensional transformations.
– Ability to simulate probability problems.
Course Info
Lectures :
• All Eng
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Friday
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15:30 – 18:30
(Hybrid-CZ12)
Course lectures in Microsoft PowerPoint
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The pdfs will be uploaded to Microsoft Teams.
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Preview the notes uploaded before coming to the class.
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Undergrad TA’s will also be arranged to help.
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Heavy use of programming in assignments
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We will provide additional tutorials if you are not confident
Text-Books :
1. Applied Statistics and Probability for Engineers, Sixth Edition,
Douglas C. Montgomery and George C. Runger, ISBN : 13
9781118539712
2. Intuitive Probability and Random Processes Using MatLab Steven M. Kay, 2016, ISBN-13: 978-0-387-24157-9"
Google Class
• Microsoft Teams Course Code : 1ibauzv
– Use the class code to add yourself to the
class.
– We collect exams, assignments, and
quizzes from this platform.
• You will need a Medipol email address to be
part of Microsoft Teams.
– It is your responsibility to join the MS Teams.
– No excuses will be accepted that you do not
have access to MS Teams.
• Announcements will be made through MS
Teams.
Assignments
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5 Assignments in total, 25 % of the overall grade
Individual attempt
Usually theory + simulations
Academic misconduct will be penalized.
Software tools for the similarity detection
Online submission via MS Teams
Usually due by the evening.
No late submissions will be accepted.
– It will be impractical to keep the door open when there are
more than 100 students.
– So do not send emails to the TA
Assignment Submission
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Submission via PDF.
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This makes our grading easier. Other formats will be rejected. We can’t open them in Google Class.
You can learn ShareLatex for easy typing (10% Assignment bonus).
Scanning your hand writing is OK too but low quality scans will receive lower marks.
• TA’s do not have time to figure out what you might have there.
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1. Your final answer sheet must be in PDF format, not word, not jpeg, not Powerpoint.
2. You can use PowerPoint since it is easy, very flexible and it provides easy drawing.
3. Your hand-writing is fine too, but it has to be clearly scanned and converted to PDF
format.
3. Your final submission should only be electronic submission. No paper submissions.
4. Zip the Codes and the PDF file together. No .rar or other compression types.
5. Naming conventions:
For the PDF file: YourDeptInitial_NameLastName_HWNumber.pdf, for example,
IE_HasanKurt_HW2.pdf,
For the Zip file : IE _HasanKurt_ HW2.zip,
For the Code files : IE _HasanKurt_ HW2Q5Partc.m. Here, we add question number
and its part to the naming convention. For each part we should submit a different code
file.
6. Do not embed codes in PDF file.
7. Department initials are CEE, CoE, BME, EEE, IE.
8. Failure to follow the submission requirements will void your submission as TAs do
not have time to sort your non-conforming submissions.
•
Half-an-hour before the submission, stop your work and make sure
you are compliant with the submission guidelines.
Quizzes and Participation
• We will have more than 5 pop-quizzes.
• Make sure you comprehend the
previous and current topics in the
class.
• You will also be randomly asked
simple questions during the class to
ensure your participation.
• Quizzes and participation are 10% for
the overall grading.
Exams
1 Midterm Exam
: 25%
1 Final Exam
: 40%
All are closed book exams,
No formula sheets nor calculators nor
phones are allowed.
• We typically give you a formula sheet
as part of the exam.
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Overall Marking
Activity
Count
Each
Total %
Assignments
5
5%
25
Quizzes + Participation
5-10
TBD
10
Midterm
1
20%
25
Final
1
40%
40
Couple Points
• Follow the course from the beginning and try not to
miss even a single class.
• In case you miss classes,
– Make up the missing class through similar topics on
YouTube.
– YouTube has a rich content for Signals and Systems.
• Make sure you follow the class during online delivery.
Do not let Internet to disrupt your education and
hence your future career.
• Medical reports are not alone sufficient for the exam
make-up. The prof needs to be convinced too.
• Make sure you are muted during the class. If you
have a question you can simply ask.
• In general, you need good math skills.
• Calculus II is now the pre-requisite for this course.
Budgeting Your Time
• Time is like money – invest it wisely
• Education is an expensive
investment – requires responsible
management
• Learning is a lot of work at the
beginning, and it’s not much fun
• Often, after even a short period of
time, learning will become a joy and
raise your self-esteem
• Learning and understanding new
things can be downright exciting
Budgeting Your Time – An Example of Weekly
Activities
There are still 68 hours left for classes and school work!
For this class ECTS (AKTS) amount is 6. So you need to
spend 6x25 hrs = 150 hrs per semester, or 10 hours per
week.
Budgeting Your Time – An Example of Weekly
Activities (continued)
• How to budget the remaining 68 hours
– Typically 16 credit hours of courses in a
semester
– Average of 2 to 3 hours of study per one
hour of class time (16x2=32; 16x3=48)
– Some classes are more demanding than
others
– Still have 20 to 36 hours a week in your
budget to allocate at your own discretion
Daily Studying and Preparation
• Start from the very first day of class
• Read the materials ahead of time
• Review class materials later on the same
day
• Attend class regularly
• Get help right away
– See professors during the designated office
hours or make an appointment to see them
– See the class TA
– Join undergrad TA session
• Get to know your professors and visit them
often
Daily Studying and Preparation
(continued)
• Take good notes
– Don’t use loose papers to take notes
– Study your notes at least an hour or
two the same day you take them
– Understand all the concepts and
ideas that were discussed in class
before you attempt to do your
homework assignment
– Don’t try to find an example that
resemble the assignment problem
– There is no shortcut to learning
Daily Studying and Preparation
(continued)
• Take good notes
– Write notes in the textbook or printed
slides margins while studying
– Keep all engineering books
– May want to type a summary sheet of
all important concepts and create an
electronic file
Then you can use the find command to look up
selected terms or topics
Daily Studying and Preparation
(continued)
• Select a good study place
– Good lighting and comfortable
– No distraction
– Have roommates who have similar
studying habits
– Maintain a clean desk and avoid
having a picture of your sweetheart in
front of you!
Don’t want to daydream as you are studying
Daily Studying and Preparation
Not a good way to study!
Daily Studying and Preparation
A good way to study!
Daily Studying and Preparation
(continued)
• Form study groups
– Need to study on your own first and
then get together with your classmates
to discuss and explain key ideas and
concepts to each other
– Group should agree on the above
process
– Be an active learner
– Don’t be a passive learner
Daily Studying and Preparation
(cont.)
• Prepare for your exams
– There is no substitution for daily studying
– Don’t wait till the night before the exam to
study
– The night before the exam, spend a few
hours reviewing your notes and sample
problems
– Ask your instructor ahead of time what
type of exam it will be; how many
questions there will be; and so on
– Ask your instructor for suggestions to help
you prepare better for the exam
Prepare for Your Exam
• Have a good night sleep
• Read and understand the questions
first, ask your instructor for
clarification if needed
• Answer the easy questions first and
then comeback to more complicated
questions
• If you have test anxiety, in order to
reduce it, prepare well and consider
timing yourself when doing your
homework problems
Get Involved with an Engineering
Organization
Professional organizations offer the
following benefits:
• Conduct conferences and meetings to
share ideas in research and
development
• Publish technical journals, books,
and magazines
• Offer short courses
• Advise federal, state, and local
government on technology related
public policies
Other Considerations
• Do volunteer work
– Not only you would feel good about
yourself, you will gain a sense of
satisfaction and feel connected to your
community
• You can help new undergrads.
• Be a responsible citizen
– Vote
– Play an active role in local, state, or
government
• Get to know your classmates
• Get to know an upper-division
engineering student