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COMSATS UNIVERSITY ISLAMABAD, LAHORE CAMPUS

Defence Road, Off Raiwind Road, Lahore

COURSE HANDBOOK

1 Course Title Statistical and Probability Theory

2 Course Code MTH 262
3 Credit Hours 3(3,0)
4 Semester Fall 2022
5 Resource Person Dr. Irfan Aslam
6 Supporting Team Members NA
7 Contact Hours (Theory) 3 hours per week
8 Contact Hours (Lab) Not Applicable
9 Office Hours Will be informed later
10 Course Introduction

A student completing this class is expected to develop not only the

logical reasoning but also the technical skills to apply the probability
tools and techniques in real world scenarios.

11 Learning Objectives
a. Know how to work with data: collection, summarization,
presentation etc.
b. Know how to describe distributions using graphs and numerical
descriptors.
c. Demonstrate an understanding of basic principles of probability,
and sample spaces.
d. Demonstrate understanding of conditional probability,
independence and Bayes rule.
e. Know the basic discrete distributions (Binomial, Geometric,
Negative Binomial and Poisson) and how to work with them.
f. Know the basic continuous distributions (Uniform, Normal,
Student t, Gamma and Beta) and know how to work with them
g. Understand how to apply fundamental concepts such as the
cumulative distribution function, expectations, and distributions
for functions of random variables.
h. Know how to apply the Central Limit Theorem.
i. Be able perform hypothesis tests in the context of a single
population sample.
j. Know how to perform regression and correlation analyses.

12 Course Contents
Introduces the essentials of probability theory and elementary
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statistics. Lectures and assignments greatly stress the manifold

applications of probability and statistics to computer science. Contents
include: descriptive statistics, graphical, pictorial and tabular methods,
and measures of location and of variability; sample space and events,
probability axioms, and counting techniques; conditional probability
and independence, law of total probability, and Bayes' theorem;
discrete random variables, distribution functions and moments;
bivariate probability distributions, marginal probability and conditional
probability distributions; uniform binomial, negative binomial,
multinomial, geometric hyper-geometric, multi-hyper-geometric and
Poisson probability distributions; continuous random variables,
densities and moments, uniform, uniform, normal, gamma, and
exponential probability distributions; hypothesis testing and p-values,
and applications for the mean: Simple and multiple linear Regression
and correlation analysis.
13 Lecture/Lab Schedule
Weeks Topic of Lecture Reading
Assignment
Week 1  Introduction to statistics and statistical Will be discussed in
methods, Deterministic and class after each
Probabilistic models, and statistical lecture.
thinking.
 Data: Types, collection methods, biased
and unbiased estimators, population and
sample, bias and sampling error.
Week 2  Data presentation: frequency Will be discussed in
distributions, tabulation, and graphical class after each
presentations. lecture.
 Measure of central tendency:
arithmetic, geometric, and harmonic
means for both grouped and un-
grouped data
Week 3  Measure of central tendency: median Will be discussed in
and mode for both grouped and un- class after each
grouped data. Quintiles: quartiles, lecture.
deciles, and percentiles etc.
 Measure of dispersion: Range, quartile
deviations, variance and standard
deviation.
Week 4  Introduction to decision making under Will be discussed in
uncertainty class after each
 Sample space, events , probability and lecture.
rules of Probability
Week 5  Independence of events. Will be discussed in
 Conditional Probability class after each
lecture.
Week 6  Random variables, types of random Will be discussed in

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variable, and their distributions class after each

 Discrete Bivariate, marginal and lecture.
conditional probability distributions
Week 7  Continuous Bivariate, Will be discussed in
 Marginal and conditional probability class after each
distributions lecture.
Week 8  Binomial Probability distributions Will be discussed in
 Hyper-geometric class after each
lecture.
Week 9  Poisson Probability distribution and its Will be discussed in
properties class after each
 Geometric and Negative Binomial lecture.
probability distributions
Week 10  Normal distributions Will be discussed in
 Normal approximation to the Binomial class after each
probability distribution lecture.
Week 11  Exponential distribution and its Will be discussed in
applications class after each
 Gamma distribution and applications lecture.
Week 12  Testing of hypothesis for population
mean: one sample
 Testing of hypothesis for population
proportion: one sample
Week 13  Testing of hypothesis for population Will be discussed in
means: two samples class after each
lecture.
Week 14  Testing of hypothesis for population Will be discussed in
proportions: class after each
lecture.
Week 15  Simple and multiple linear regression Will be discussed in
 Correlation analysis class after each
lecture.
Week 16 Revision
14 Course Assessment
The assessment of this module shall have following breakdown structure
First Sessional Test 10%
Second Sessional Test 15%
Quizzes/Assignments 25%
Terminal Examination 50%
The minimum pass marks for each course shall be 50%. Students obtaining less than 50% marks
in any course shall be deemed to have failed in that course. The correspondence between letter
grades, credit points, and percentage marks at CIIT shall be as follows:
Grades Letter Grade Credit Points Percentage Marks

A ( Excellent) 4.0 90and above

A- 3.7 85-89
B+ 3.3 80-84
B (Good) 3.0 75-79

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B- 2.7 70-74
C+ 2.3 65-69
C (Average) 2.0 60-64
C- 1.7 55-59
D (Minimum passing) 1.3 50-54
F (Failing) 0.0 Less than 50
Note: The marks to be assigned to students shall be in whole numbers and are not same as
followed in the annual system of Lancaster University.

15 Assessment Schedule
Week 2 1st Assignment Week 2 1st Quiz
Week 4 2nd Assignment Week 4 2nd Quiz
Week 7 3rd Assignment Week 7 3rd Quiz
Week 9 4th Assignment Week 9 4th Quiz

16. Format of Assignment

Will be informed in the class.
17. Text Book 1. Probability & Statistics for Engineers &
Scientists by Ronald E. Walpole, Raymond H.
Myers, Sharon L. Myers , and Keying Ye, 8th
Edition

18. Reference Books 2. Probability and statistics for computer

scientists by Michael Baron.
3. Probability and statistics for computer
science by James L. Johnson

19. Plagiarism
Plagiarism involves the unacknowledged use of someone else’s work, usually in coursework, and
passing it off as if it were one’s own. Many students who submit apparently plagiarised work
probably do so inadvertently without realising it because of poorly developed study skills,
including note taking, referencing and citations; this is poor academic practice rather than
malpractice. Some students, particularly those from different cultures and educational systems,
find UK academic referencing/acknowledgement systems and conventions awkward, and proof-
reading is not always easy for dyslexic students and some visually-impaired students. Study skills
education within programmes of study should minimise the number of students submitting poorly
referenced work. However, some students plagiarise deliberately, with the intent to deceive. This
intentional malpractice is a conscious, pre-mediated form of cheating and is regarded as a
particularly serious breach of the core values of academic integrity. The Dual Degree
Programme has zero tolerance for intentional plagiarism.

Plagiarism can include the following:

1. collusion, where a piece of work prepared by a group is represented as if it were the
student’s own;
2. commission or use of work by the student which is not his/her own and representing it as
if it were, e.g.:
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a. purchase of a paper from a commercial service, including internet sites, whether

pre-written or specially prepared for the student concerned
b. submission of a paper written by another person, either by a fellow student or a
person who is not a member of the university;
3. duplication (of one’s own work) of the same or almost identical work for more than one
module;
4. the act of copying or paraphrasing a paper from a source text, whether in manuscript,
printed or electronic form, without appropriate acknowledgement (this includes quoting
directly from another source with a reference but without quotation marks);
5. submission of another student’s work, whether with or without that student’s knowledge
or consent;
6. Directly quoting from model solutions/answers made available in previous years;
7. cheating in class tests, e.g.
a. when a candidate communicates, or attempts to communicate, with a fellow candidate
or individual who is neither an invigilator or member of staff
b. copies, or attempts to copy from a fellow candidate
c. attempts to introduce or consult during the examination any unauthorised printed or
written material, or electronic calculating, information storage device, mobile phones
or other communication device
d. Personates or allows himself or herself to be impersonated.
8. Fabrication of results occurs when a student claims to have carried out tests, experiments
or observations that have not taken place or presents results not supported by the evidence
with the object of obtaining an unfair advantage.
These definitions apply to work in whatever format it is presented, including written work,
online submissions, group work and oral presentations.

20. Attendance Policy

Every student must attend 80% of the lectures/seminars delivered in this course and 80% of the
practical/laboratory work prescribed for the respective courses. The students falling short of
required percentage of attendance of lectures/seminars/practical/laboratory work, etc., shall not
be allowed to appear in the terminal examination of this course and shall be treated as having
failed this course.

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