# Intro. Probability Theory – MATH 4510/5510 – SUMMER

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: M-F 01:00PM – 02:35PM
Location: GUGG 2
Office hours: See details here

Homework: 25% – Weekly homework (you must turn them in)
Participation: 20%
Midterm I (06/10): 25%
Final (to be announced) : 30%

Homework sets

Second week assignment – due to 06/10 – set of exercises is on Canvas

First week assignment – Due to 06/03

Textbook

## A First Course in Probability

by Sheldon Ross

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Course notes

## Limit Theorems in Probability Theory – MATH 4510/5510 – SUMMER

The Law of Large Numbers and the Central Limit Theorem

## Normal Distribution – MATH 4510/5510 – SUMMER

Normal distribution

## Uniform and Exponential Distributions – MATH 4510/5510 – SUMMER

Uniform distribution, Exponential distribution, Memoryless distributions.

## Geometric Distribution – MATH 4510/5510 – SUMMER

Geometric distribution

## Poisson Distribution – MATH 4510/5510 – SUMMER

Poisson distribution

## Binomial Distribution – MATH 4510/5510 – SUMMER

Introduction to probability distributions and binomial distribution

## Variance and Chebyshev’s inequality – MATH 4510/5510 – SUMMER

Introduction to Variance and Chebyshev’s inequality.

Expected value

## Discrete and Continuous Random Variables – MATH 4510/5510 – SUMMER

Introduction to random variables, CDF, density functions and independence for random variables

## Bayes’s Formulas and Independent Events – MATH 4510/5510 – SUMMER

Monty Hall Dilemma, Bayes’s Formulas and Independent Events

## Conditional Probabilities and the Multiplication Rule – MATH 4510/5510 – SUMMER

Introduction to conditional probability theory and the multiplication rule. Use of probability in court

## Axioms of Probability – MATH 4510/5510 – SUMMER

Sample spaces, events and probability measure.

## Addition Principle and the Inclusion-Exclusion formula – MATH 4510/5510 – SUMMER

Addition and Subtraction principles of counting. Inclusion-Exclusion formula.

## Equally Likely outcomes and Multiplication Principle – MATH 4510/5510 – SUMMER

Defining probability for random experiments with equally likely outcomes, and the Multiplication Principle