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 10:20 AM – 11:10 AM
Location: Zoom
Office hours: See details here
Grading
Homework: 25% – Weekly homework (you must turn them in)
Midterm I (02/15): 20%
Midterm II (04/14): 25%
Final (to be announced) : 30%
Homework sets
Homework #9 (turn in the bold ones)
Chapter 5 – Problems: 5.2, 5.8, 5.13, 5.15 (hint: transform X into a standard normal and use the table of probabilities for the standard normal)
Due to 04/26
Homework #8: Study Guide on Probability Distributions.
Due to 04/09
Homework #7 (turn in the bold ones)
Chapter 4 – Problems: 4.23, 4.24, 4.26, 4.38 +(extra question posted on canvas)
Chapter 4 – Theoretical Exercises: 4.4, 4.7, 4.8
Due to 04/02
Homework #6 (turn in the bold ones)
Chapter 4 – Problems: 4.1, 4.4, 4.5, 4.6, 4.14, 4.20, 4.21
Due to 03/19
Homework #5 (turn in the bold ones)
Chapter 3 – Problems: 3.15, 3.16, 3.31, 3.43, 3.46
Chapter 3 – Theoretical exercises: 3.8, 3.25
Due to 03/12
Homework #4 (turn in the bold ones)
Chapter 3 – Problems: 3.1, 3.2, 3.4, 3.9, 3.10, 3.11, 3.18
Chapter 3 – Theoretical Exercises: 3.1, 3.2, 3.5
Due to 03/05
Homework #3 (turn in the bold ones)
Chapter 2 (8th, 9th and 10th editions)
Problems: 3, 38, 48
Theoretical Exercises: 13,15.
Due to 02/15
Homework #2 (turn in the bold ones)
Chapter 2 (8th, 9th and 10th editions)
Problems: 1 – 11, 2,8,14
Theoretical Exercises: 5,6,11, 12, 16
Due to 02/07
Homework #1: You must turn in the bold ones
From Chapter 1
Problems : 1 to 11. Turn in problem 4
Theoretical exercises: 3,4,5,6,8
Due to 01/29
All problems refer to our textbook.
Textbook
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Course notes

The Joint Cumulative Distribution – MATH 4510/5510
Introduction to joint distributions


Review for Midterm II – MATH 4510/5510
Review of all important concepts for the Midterm II

The Continuous Uniform Random Variable – MATH 4510/5510
Definition and properties of uniformly distribution random variables over intervals

Continuous Random Variables – MATH 4510/5510
Introduction to Continuous Random Variables

How to prepare for Midterm II and other comments – MATH 4510/5510
Tips and comments about Midterm II

The Cumulative Distribution Function – MATH 4510/5510
The Cumulative Distribution Function and some properties



Binomial Distribution – MATH 4510/5510
One of the most important discrete distributions

Variance and Standard deviation – MATH 4510/5510
Introduction to variance and standard deviation

Expected Value of Sums of Random Variables – MATH 4510/5510
Expected value of sums of random variables and the substitution formula

Expected value and Investments – MATH 4510/5510
Building a mathematical model to understand the impacts of deviating too much from the expected value

Expected value of a function of a random variable – MATH 4510/5510
Formula to compute expected value of a function of a random variable

Expected Value – MATH 4510/5510
Expected value of discrete random variables and connection with Law of Large Numbers

Random Variables – MATH 4510/5510
General definition of random variables and examples in the discrete case

Monty Hall Dilemma – MATH 4510/5510
Solving and discussing the famous Monty Hall dilemma

The m points problem – MATH 4510/5510
An Important historical problem involving probability theory



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

Midterm I – Review I – MATH 4510/5510
Comments about Midterm I and theoretical review

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!