# Intro. Probability Theory – MATH 4510/5510

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

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

## A First Course in Probability

by Sheldon Ross

Other books I like

by Henk Tijms

by Rick Durrett

Course notes

## Final Review – MATH 4510/5510

General comments on the final and review on the theoretical part with examples.

## Central Limit Theorem – MATH 4510/5510

The Central Limit Theorem and applications.

## 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

## Midterm II – Recap – Part I – MATH 4510/5510

Preparing for the Midterm II.

## Poisson Distribution – MATH 4510/5510

Introducing the Poisson Distribution.

## Geometric Distribution – MATH 4510/5510

Introducing the Geoemtric Distribution.

## Binomial Distribution – MATH 4510/5510

Introducing the Binomial Distribution.

## 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.

## Independence of Events – MATH 4510/5510

Independence of events

## Midterm I Recap – MATH 4510/5510

Recap for Midterm I

## 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

## Axioms of Probability – MATH 4510/5510

Axioms of Probability

## Sample Space – MATH 4510/5510

Sample Space, Events and first definitions

## Combinations – MATH 4510/5510

Combinations and the Binomial Theorem

## Basic Principle of Counting – MATH 4510/5510

(Generalized) Basic Principle of Counting and Permutations