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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) 8535Secretary/TA Shazia Zafar & Noreen Sohail / TBA TA Office HoursTBA Course URL (if any) 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% Examinaon 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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