# 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 (to be announced) : 30%

Homework sets

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

## Central Limit Theorem – MATH 4510/5510

Central Limit Theorem and little about histograms

## The Law of Large Numbers – MATH 4510/5510

The Law of the large numbers: statement, proof and how to use it

## Independent Random Variables – MATH 4510/5510

Introduction to independence for random variables

## The Joint Cumulative Distribution – MATH 4510/5510

Introduction to joint distributions

## Normal Distribution – MATH 4510/5510

Normal Distribution

## 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

## The Cumulative Distribution Function – MATH 4510/5510

The Cumulative Distribution Function and some properties

## Poisson Distribution – MATH 4510/5510

Introduction do the Poisson Distribution

## Geometric Distribution – MATH 4510/5510

Introduction do the Geometric Distribution

## 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

## Independent Events – MATH 4510/5510

Introduction to Independent Events

## Bayes Formulas – MATH 4510/5510

Bayes formulas to compute probabilities

## 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