INTRODCUTION TO Probability

SPRING ‘22

Course Logistics

Course Outline

Lectures: MW 11:30-12:45

Lectures

Lecture 1 - Introduction

Lecture Video

Class Notes

Suggested Exercises: Video Links Below

Lecture 2 - Basics of Counting

Lecture Video

Class Notes

Suggested Exercises:(Chapter 1: pg 15) 1-5, 6, 7, 9, 10

                                   (Chapter 1: pg 17) 2, 4, 6 

Lecture 3 - Permutations and Combinations

Lecture Video

Class Notes

Suggested Exercises:(Chapter 1: pg 15) 11, 12, 14, 16, 18, 19, 23, 25

                                   (Chapter 1: pg 17) 8, 9, 12, 13

 Lecture 4 - Axioms of Probability

Lecture Video

Class Notes

Suggested Exercises:(Chapter 1: pg 48) 1, 2, 3, 5, 8

                                   (Chapter 1: pg 52) 1, 4, 10, 11               

Lecture 5 - Applications of Axioms of Probability

Lecture Video

Class Notes

Suggested Exercises: (Chapter 2: pg 49) 9,12,13,15

Lecture 6 - Conditional Probability

Lecture Video

Class Notes

Suggested Exercises: (Chapter 2: pg 49) 21,23,24,25,27

                                   (Chapter 2: pg 52) 12,13,19              

Lecture 7 - Conditional Probability & Independence

Lecture Video

Class Notes

Suggested Exercises: (Chapter 3: pg 97) 1, 5,6,7,9,1214,15

                                   (Chapter 3: pg 52) 4,5,7             

Lecture 8 - Bayes Theorem

Lecture Video

Class Notes

Suggested Exercises: (Chapter 3: pg. 97) 16,18,19,23,29,31

Lecture 9 - Independence

Lecture Video

Class Notes

Suggested Exercises: (Chapter 3: pg. 100) 32, 33,36, 40,51,53, 55, 58, 74

                                    (Chapter 3: pg. 106) 5, 7, 9, 18, 22

Lecture 10 - Random Variables

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 1,4,7,8,13,14,17,21

Lecture 11 - Expectation and Variance

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 25,27,28,30,32

 Lecture 12 - Bernoulli and Binomial Distributions

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 33,35,39,40,44,46,48,49.50

Lecture 13 - The Poisson Distribution

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 51,52,54,55,56,57

Lecture 14 - Poisson Distribution and the Poisson Approximation

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 58,59,61,63,64,65,68

Lecture 15- Geometric Distribution

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 71,72,73,74,75

Lecture 16 - Negative Binomial and Hypergeometric Distributions

Lecture Video

Class Notes

Suggested Exercises: (Chapter 4: pg. 163) 78,79,80,82,83

Lecture 17 - Continuous Radom Variables

Lecture Video

Class Notes

Suggested Exercises: (Chapter 5: pg. 212) 1,3,4,5,8,9

Midterm Exam

Lecture 18 - Uniform Radom Variable

Lecture Video

Class Notes

Suggested Exercises: (Chapter 5: pg. 212) 10,11,12,13,14

Lecture 19 - Normal/Gaussian Radom Variables I

Lecture Video

Suggested Exercises: (Chapter 5: pg. 212)  15,17,19,20,21

Lecture 20 - Normal/Gaussian Radom Variables II

Lecture Video

Suggested Exercises: (Chapter 5: pg. 212) 15,17,19,20,21

Lecture 21 - Normal Approximation to the Binomial

Lecture Video

Suggested Exercises: (Chapter 5: pg. 212) 22,23,24,25,27

Lecture 22 - Exponential Random Variables

Lecture Video

Suggested Exercises: (Chapter 5: pg. 212) 32,33,34,35

Lecture 23 - Interarrival Time and Hazard Rate Function

Lecture Video

Suggested Exercises: (Chapter 5: pg. 212) 36,37,38

Lecture 24 - Jointly Distributed Random Variables

Lecture Video

Suggested Exercises: (Chapter 6: pg. 271) 1,3,6,7,8,9,10  

Lecture 25 - Joint Distribution and Independence

Lecture Video

Suggested Exercise: (Chapter 6: pg. 271) 12,13,15,17,19,21,23,24

Lecture 26 - Sums of i.i.d Random Variables

Lecture Video

Suggested Exercise: (Chapter 6: pg. 271) 27,29,32,33,34,35,40

Lecture 27 - Central Limit Theorem and Simulation

Lecture Video

Suggested Exercise: (Chapter 8: pg. 390)    1,2,3,4,5,6,7

                                   (Chapter 10: pg. 430) 2,3,4,5

Useful Links

The Magical Mind of Persi Diaconis: http://chronicle.com/article/The-Magical-Mind-of-Persi/129404/

The Search for Randomness (Video Lecture): https://www.youtube.com/watch?v=xit5LDwJVck

Counting of Urns and Balls: www.johndcook.com/TwelvefoldWay.pdf

Computer Stuff (Codes are in MATLAB)