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Lahore University of Management Sciences
MATH 230 – Probability
FALL 2019-2020
InstructorShaheena BashirRoom No.9-151 Office HoursMonday/Wednesday (11:00 am-12:00 noon or by appointment) Emailshaheena.bashir@lums.edu.pkTelephone 8535Secretary/TA Shazia Zafar & Noreen Sohail / TBA TA Office HoursTBA Course URL (if any)https://lms.lums.edu.pk/portalCourse BasicsCredit Hours3Lecture(s)Nbr of Lec(s) Per Week2Duration75minRecitation/Lab (per week)Nbr of Lec(s) Per WeekDurationTutorial (per week)Nbr of Lec(s) Per Week1Duration75 minCourse DistributionCoreCore course for all SSE majors ElectiveOpen for Student Category All studentsClose for Student CategoryNone
COURSE DESCRIPTION
This is a first course in probability which provides basic concepts related to modelling of chance events in practicallife. It provides preparation for further courses in stochastic processes, statistics, statistical mechanics and anunderstanding of the probability concepts essential for students who want to pursue studies in physical sciences,social sciences, economics, and engineering. The course starts with an introduction of probability terms andmethods of computing simple and conditional probabilities. The concepts of discrete and continuous randomvariables are covered. Special discrete and continuous probability distributions are explored with their real lifeapplications.
COURSE PREREQUISITE(S)
MATH 101-Calculus I
Lahore University of Management Sciences
COURSE OBJECTIVES
Student will learn what probability is
Learn different concepts of probability & different ways of expressing probability
Learn how probability is helpful in quantification & modelling of everyday chance events to provide scientifically valid conclusions.
Learning Outcomes
Having successfully completed the course the students will be able to
Explain the concepts of probability, including conditional probability
Explain the concepts of random variable, probability distribution, distribution function, expected value, variance and higher moments, and calculate expected values and probabilitiesassociated with the distributions of random variables
Define basic discrete and continuous distributions, be able to apply them
Understand & apply Central Limit Theorem in different problems.
Grading Breakup and Policy
Assignment(s):Home Work:
Quiz(s): (Best 5 out of 7) 30%
Class Participation: Attendance:
Midterm Examination: 30%
Project:
Final Examination: 40%
Examinaon Detail
Midterm Exam Yes/No: YesCombine Separate: SeparateDuration: 75minPreferred Date: 9:30 a.m – 11:15 a.m (October 28, 2019)Exam Specifications: Closed book/Closed notes/ calculator allowedFinal Exam Yes/No: YesCombine Separate: SeparateDuration: 150minExam Specifications: Closed book/Closed notes/calculator allowed
What you get out of the course depends on what you put into the
course.
Lahore University of Management Sciences
Quizzes
Quizzes will be held in the first 10 – 15 minutes of the class. The purpose of the quizzes is to assess your participation.
Missed Quiz Policy:
Missed quiz earn a mark of zero. No exceptions, no medical certificate or other documentation accepted.
Best 5 out of 7 quizzes will be considered.
Term Test
Term test will be held in the lecture room on the specified date (i.e 9:30 a.m – 11:15 a.m (October 28, 2019). There is no extra time for late entrants.
Tentative Lecture Schedule
SerialWeek ofTopicTextbookReference
1.02-SeptIntroduction of RandomnessOverview of Set Theory.Chapter 1Basic Principles of Counting 2.09-SeptPermutation, Combination, Multinomial Coefficients3.16-SeptSample Space & Events Chapter 2 Axioms of ProbabilityProbability of Events4.23-SeptConditional Probability & IndependenceChapter 3Conditional ProbabilityLaw of Total Probability; Bayes’s TheoremIndependent Events5.30-SeptRandom VariablesDiscrete Random Variables; Expected Value; Expectation of a functionof Random Variables; VarianceChapter 46.07-OctBernoulli & Binomial Random Variable; Poisson Random Variable7.14-OctOther Discrete Distributions.8.21-OctContinuous Random Variable
Review for Mid-Term
Chapter 59.28-Oct
Mid Term:
9:30 a.m – 11:15 a.m (October 28, 2019).
(Includes material covered till Section 4.8)
Uniform Random Variable
Lahore University of Management Sciences
10.04-NovNormal Random Variables11.11-NovExponential Random Variables12.18-NovJoint Distributions; Conditional Distributions; Discrete Case,Continuous CaseChapter 613.25-NovProperties of ExpectationChapter 714.02-DecLimit Theorems.Central Limit Theorem and applicationsChapter 815.09-Dec
Review for Final Exam
16.
Final EXAM
Textbook(s)/Supplementary Readings
Required Textbook:
A First Course in Probability, 9th Edition, Sheldon Ross The required text will be supplemented with notes and exercises.
Additional References:
Introduction to Probability Models, 10th Edition, Sheldon Ross Probability for Dummies, 2006. Deborah Rumsey.

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