Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits
Ongoing course
Time: MWF 12:20 PM – 01:10 PM
Location: Zoom (First two weeks) – ECCR 108
Office hours: See details here
Grading
Homework: 25% – Weekly homework (you must turn them in)
Midterm I (02/18): 20%
Midterm II (04/01): 25%
Final (05/04) : 30%
Homework sets
Assignment 10 (Due to 04/25)
Chapter 6
6.10,6.15,6.17,6.20,6.31,6.32
Assignment 9 (Due to 04/21)
Chapter 5
Problems: 5.14,5.15,5.16,5.18,5.19,5.28
Chapter 6
Problems: 6.1,6.6,6.8
Assignment 8 (due to 04/11)
Chapter 5
Problems: 5.2, 5.4, 5.6, 5.11, 5.13
Assignment 7 (due to 04/01)
Chapter 3
3.23, 3.37, 3.58
Chapter 4
Problems 4.21,4.25,4.30,4.38,4.53
Theoretical Exercises 4.13, 4.35
Assignment 6 (due to 03/14) – Chapter 4
Problems: 4.30, 4.35, 4.38, 4.41
Theoretical Exercises: 4.7
Assignment 5 (due to 03/07)
Problems: 4.1, 4.2, 4.5, 4.13, 4.21, 4.25
Theoretical Exercises: 4.4
Assignment 4 (Due to 02/11) – Chapter 3
Problems: 13, 15, 16
Theoretical Exercises: 1,5
You must turn in all the exercises
Assignment #3 (Due to 02/04) – Chapter 2
Problems: 23, 25, 29, 35
Theoretical Exercises 13
You must turn in all the exercises
Assignment #2 (Due to Jan 28th) – Chapter 2
Problems: 1 – 11, 2*,8*,14*
Theoretical Exercises: 5*,6,11*, 12, 16
You must turn in all starred ones.
Assignment #1 (Due to Jan 21st) – Chapter 1
Problems: 2,3,4,7,10*,11,13,16*,21,22*
Theoretical exercises: 1*,8*,11*
You must turn in all starred ones.
All problems refer to our textbook (ninth edition)
Textbook
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Course notes
Final Review – MATH 4510/5510
General comments on the final and review on the theoretical part with examples.
Law of Large Numbers – MATH 4510/5510
Introduction to independent random variables, properties of independent random variables.
Independent Random Variables – MATH 4510/5510
Introduction to independent random variables, properties of independent random variables.
Joint distributions – MATH 4510/5510
Joint distributions, Joint cumulative distribution functions, joint pmfs, jointly continuous random variables.
Histogram and the Normal distribution – MATH 4510/5510
Definition of histograms and the normal distribution.
Uniform Distribution over [a,b] – MATH 4510/5510
Continuous random variables that are Uniformly distributed over intervals
Continuous Random Variables – MATH 4510/5510
Introduction to Continuous Random Variables
Variance and Standard deviation – MATH 4510/5510
Measuring variability. Variance, standard deviation and Chebyshev’s inequality.
Pitfall for Averages – MATH 4510/5510
Can we make decisions based only on the expected value?
Expected Value of sums of random variables – MATH 4510/5510
Deriving a formula to compute expected value of functions of random variables.
Expected Value of functions of random variables – MATH 4510/5510
Deriving a formula to compute expected value of functions of random variables.
Expected Value – MATH 4510/5510
Introduction to Expected value, Law of Large Numbers and expected value as weighted average.
Random Variables – MATH 4510/5510
Random Variables, Discrete Random Variables, Probability Mass Function of random variables
Gambler’s Ruin Problem – MATH 4510/5510
Solving the classic and the biased version of the Gambler’s Ruin Problem.
Bayes’ Formulas and Gender Bias – MATH 4510/5510
Bayes formulas to compute probabilities and using probability to understand gender bias
The Conditional Measure – MATH 4510/5510
Investigating the conditional probability and an example from genetics
Conditional Probability – Part II – MATH 4510/5510
Introduction to conditional probability
Conditional Probability – Part I – MATH 4510/5510
Introduction to conditional probability
Probability as a measure of belief – MATH 4510/5510
Probability as a measure of belief
Probability measure as a continuous set function – MATH 4510/5510
Probability measure as a continuous set function. Increasing and decreasing events.
Sample spaces with equally likely outcomes – MATH 4510/5510
Sample spaces with equally likely outcomes
Basic Principle of Counting – MATH 4510/5510
(Generalized) Basic Principle of Counting and Permutations
Introduction to the course – MATH 4510/5510
General comments about probability theory and our course!