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

*4.13, 4.35*

**Theoretical Exercises****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!