Lahore University of Management Sciences
DISC 203 – PROBABILITY AND STATISTICS
Fall 2023
Instructor
Room No.
Office Hours
Email
Telephone
Secretary
TA Office Hours
Course URL (if any)
Muhammad Asim/ Abid Raza Khan
TBA
TBA
Muhammad.Asim@lums.edu.pk / abid.raza@lums.edu.pk
TBA
Nabeela Shahzadi <nabeela@lums.edu.pk>
TBA
https://lms.lums.edu.pk/portal
COURSE TEACHING METHODOLOGY
Teaching methodology
Lecture details
Synchronous learning
100 % live
COURSE BASICS
Credit Hours
Lecture(s)
Recitation/Lab (per week)
Tutorial (per week)
3
Nbr of Lec(s) Per Week
Nbr of Lec(s) Per Week
Nbr of Lec(s) Per Week
2
Duration
Duration
Duration
75 minutes
COURSE DISTRIBUTION
Core
Elective
Open for Student Category
Close for Student Category
Yes
Sophomore
COURSE DESCRIPTION
This course is designed to provide students majoring in management and finance with an elementary introduction to probability and statistics
with applications. Both descriptive and inferential statistics are covered. We first review techniques for organizing and presenting the raw data
and elementary probability theory. Next, we discuss various techniques to make inferences. Along with probability theory, sampling distribution
and central limit theorem shall be discussed. The idea of central limit theorem will naturally lead towards the confidence intervals and
hypothesis tests for mean and proportion. We follow this discussion with single and multiple regression analysis, model building, design of
experiments and categorical data analysis. The course also aims to give a hands-on experience with using a statistical package, R for carrying out
data analysis. The main objective of the course is to provide students with the foundations of statistical inference mostly used in business and
economics.
COURSE PREREQUISITE(S)
•
Calculus I (Math 101)
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Lahore University of Management Sciences
COURSE LEARNING OBJECTIVES (CLO)
1.
2.
3.
4.
5.
To enable students to solve problems using basic concepts of probability
To introduce students to the theory of inferential statistics
To enable students to analyze data by identifying appropriate statistical techniques, computing statistics and interpreting
results
To enable students to use R for statistical analysis of data
To enable students to present and defend their empirical analysis effectively
LEARNING OUTCOMES (LO)
1.
2.
3.
4.
5.
6.
7.
8.
9.
By the end of the course, students should be able to:
summarize the data in a useful and informative manner
use the basic concepts of probability and random variables
explain the concept of the sampling distribution of a static and describe the behavior of the sample mean
describe the foundations of classical inference involving confidence intervals and hypothesis testing and apply inferential
methods
apply modeling techniques in simple and multiple linear regression analysis
discuss critical elements in the design of a sampling experiment and analyze designed experiments using analysis of variance
analyze count data with two or more categories
use R for statistical analysis of data
defend empirical analysis effectively, both in oral and written forms
UNDERGRADUATE PROGRAM LEARNING GOALS & OBJECTIVES
General Learning Goals & Objectives
Goal 1 –Effective Written and Oral Communication
Objective: Students will demonstrate effective writing and oral communication skills
Goal 2 –Ethical Understanding and Reasoning
Objective: Students will demonstrate that they are able to identify and address ethical issues in an
organizational context.
Goal 3 – Analytical Thinking and Problem Solving Skills
Objective: Students will demonstrate that they are able to identify key problems and generate viable
solutions.
Goal 4 – Application of Information Technology
Objective: Students will demonstrate that they are able to use current technologies in business and
management context.
Goal 5 – Teamwork in Diverse and Multicultural Environments
Objective: Students will demonstrate that they are able to work effectively in diverse environments.
Goal 6 – Understanding Organizational Ecosystems
Objective: Students will demonstrate that they have an understanding of Economic, Political,
Regulatory, Legal, Technological, and Social environment of organizations.
Major Specific Learning Goals & Objectives
Goal 7 (a) – Discipline Specific Knowledge and Understanding
Objective: Students will demonstrate knowledge of key business disciplines and how they interact
including application to real world situations (Including subject knowledge).
Goal 7 (b) – Understanding the “science” behind the decision-making process (for MGS Majors)
Objective: Students will demonstrate ability to analyze a business problem, design and apply
appropriate decision-support tools, interpret results and make meaningful recommendations to
support the decision-maker
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Indicate below how the course learning objectives specifically relate to any program learning goals and
objectives.
Program Learning Goals and Objectives
Goal 1 –Effective Written and Oral
Communication
Goal 2 –Ethical Understanding and
Reasoning
Goal 3 – Analytical Thinking and Problem
Solving Skills
Goal 4 – Application of Information
Technology
Goal 5 – Teamwork in Diverse and
Multicultural Environments
Goal 6 – Understanding Organizational
Ecosystems
Goal 7 (a) – Discipline Specific Knowledge
and Understanding
Goal 7 (b) – Understanding the “science”
behind the decision-making process
Course Learning Objectives
Students get a number of opportunities to
demonstrate their ability to communicate
effectively (CLO # 5)
Students demonstrate an honest
reporting and use of data (CLO #5)
This is an important objective of the
course (CLO # 1,3,5)
Students learn to use R for data analysis
(CLO # 4)
Students work in groups on the project
Course Assessment Item
Project, Exam
NA
NA
Comprehensive coverage of topics in
elementary probability and statistics (CLO
# 1-5 & LO # 1-9)
Students apply appropriate statistical
methods to answer data-based decision
problems
(CLO # 1-5)
Assignments, Project and Exam
Project
Assignments, Project and Exam
Assignments and Project
Project
Assignments, Project and Exam
Grading Breakup and Policy
Participation in class activities: 10%
Mid-term examination: 25%
Individual Assignments: 20%
Group Project: 20% (to be completed in groups of up to 7 students. Note: Group peer assessments will be used to assess participation.)
Final Examination: 25%
Examination Detail
Midterm
Exam
Yes/No: Yes
Combine Separate: Combine
Duration: 2 hours
Exam Specifications: TBA
Final Exam
Yes/No: Yes
Combine Separate: Combine
Duration: 2 hours
Exam Specifications: TBA
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Lahore University of Management Sciences
COURSE OVERVIEW
Lecture
1
2–4
Topics
Statistics, Data and Statistical Thinking
The Science of Statistics; Types of Statistical
Applications in Business; Fundamental Elements of Statistics;
Types of Data
Methods for Describing Sets of Data using R
Graphical Methods; Summation Notation; Central
Tendency; Variability; Relative Standing; Standard Deviation;
Distorting the Truth with Descriptive Techniques
Recommended
Readings
Chapter 1
•
Understand the nature and scope of
Statistics
Chapter 2
•
Choose a suitable way of presenting
raw Statistical Data
Discuss the advantages and
disadvantages of different ways of
representing data
Calculate and interpret measures of
central tendency and variability
Describe data using R
Describe the sample space for
certain random experiments
Compute probabilities
Objectives
•
•
5–7
8 - 11
Probability
Events, Sample Spaces and Probability; Unions and
Intersections; Complementary Events; The Additive Rule and
Mutually Exclusive Events; Conditional Probability; The
Multiplicative Rule and Independent Events; Bayes’ Rule
Random Variables and Probability Distributions
Two Types of Random Variables:
Discrete Random Variables: Probability Distributions for
Discrete Random Variables; Expected Values of Discrete
Random Variables; The Binomial Random Variable; The
Poisson Random Variable
Continuous Random Variables: Probability Distributions for
Continuous Random Variables; The Uniform Distribution;
The Normal Distribution; The Exponential Distribution
Sampling Distributions: The Concept of Sampling
Distributions; Properties of Sampling Distributions:
Unbiasedness and Minimum Variance; The Sampling
Distribution of the Sample Mean
Chapter 3
•
•
•
•
Chapter 4
•
•
•
Chapter 5
•
•
•
•
12 - 13
Inference Based on a Single Sample:
Estimation with Confidence Intervals
Large-Sample Confidence interval for a Population Mean;
Small-Sample Confidence Interval for a Population Mean;
Large-Sample Confidence Interval for a Population
Proportion; Determining the sample size; Sample Survey
Designs
Tests of Hypothesis
The Elements of a Test of Hypothesis; Large-Sample Test of
Hypothesis About a Population Mean; Small-Sample Test of
Hypothesis About a Population Mean; Large-Sample Test of
Hypothesis About a Population Proportion; Observed
Significance Levels: p-values
•
Chapter 6
•
•
•
Chapter 7
Find probabilities for distributions
over discrete sets
Calculate the mean and variance of
a discrete random variable
Recognize cases where Binomial
Distribution could be an appropriate
model; compute probabilities for a
Binomial Distribution
Find probabilities for continuous
distributions
Use the key properties of the
Normal Distributions
Recognize cases where Poisson,
Uniform and Exponential
Distributions could be appropriate
and compute corresponding
probabilities
Describe properties of the sampling
distribution of sample mean
Understand and apply Central Limit
Theorem
Calculate and interpret Confidence
Intervals and Confidence Levels
Remember steps in Classical
Hypothesis testing
Describe Type I and Type II Errors
Conduct Tests of Hypothesis
according to a given situation and
interpret the results.
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15 – 16
17 – 19
Inference Based on Two Samples
Comparing Two Population Means: Independent
Sampling; Comparing Two Population Means: Paired
Difference Experiments; Comparing Two Population
Proportions: Independent Sampling; Determining the
Sample Size; Comparing Two Population Variances:
Independent Sampling
Simple Linear Regression
Probabilistic Models; Fitting the Model: The Least
Squares Approach; Model Assumptions; Assessing the Utility
of the Model: Making Inference about the Slope; The
Coefficients of Correlation and Determination; Using the
Model for Estimation and Prediction
Chapter 8
•
Apply Classical Hypothesis Testing
to compare two populations and
draw inference
Chapter 11
•
Define the concept of least squares
estimation in linear regression
Explain why correlation need not
necessarily imply causation
Evaluate the fit of a linear model
Conduct inference for the slope and
intercept parameters
Fit a linear regression model using
R, do post-estimation analysis and
explain computer output
Define the concept of Least Squares
Regression in Multiple Regression
Test the utility of a Multiple
Regression Model and use it for
estimation and prediction
Interpret the results of a Multiple
Regression Model and draw
inference
Understand how to select a model
that is appropriate for given data
Use R for Multiple Regression
Analysis
•
•
•
•
Multiple Regression and Model Building using R
20 - 25
26-28
Chapter 12
•
Multiple Regression
Multiple Regression: The Model and the Procedure;
The Least Squares Approach; Model assumptions; Inference
About the Slope Parameters; Checking the Usefulness of the
Model: R2 and the Analysis of Variance F-Test; Using the
Model for Estimation and Prediction, Residual Analysis:
Checking the Regression Assumptions
•
Model Building
The Two Types of Independent Variables:
Quantitative and Qualitative; Models with a Single
Quantitative Independent Variable; Models with Two or
More Quantitative Independent Variables; Testing Portions
of a Model; Models with One Qualitative Independent
Variable; Comparing the Slopes of Two or More Lines;
Comparing Two or More Response Curves
•
Presentations and review
•
•
•
Effectively defend statistical
analysis
Textbook(s)/Supplementary Readings
Required Text:
James McClave, P.George Benson, Terry Sincich. Statistics for Business and Economics. 13th Edition. Prentice Hall, NJ. 2018
Online resources to help you learn R:
https://www.r-project.org/
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Peer Evaluation Form
This form is a means to assess contribution of each group member towards the final project. Please be fair and honest while filling out this form.
Write the names of your group members against the numbers and then rate each of them including yourself on the following attributes. Rate
against each attribute on a scale of 1-5, at the end just sum the ratings:
5=Superior 4=Above Average 3=Average 2=Below Average 1=Weak
Attribute
Myself
1.
2.
3.
4.
Participated in
group discussions
Volunteered for
project tasks
Helped other group
members
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Lahore University of Management Sciences
Practiced active
listening & was
receptive to group
feedback
Shared resources
and added value to
the project
Contributed to EACH
stage of the project
Submitted
deliverables on time
Contributed good
quality work
Overall contribution
7