MATH 3510

# Syllabus MATH 3510

This is an attempt. Things may change as we go.

## Understanding Probability

by Henk Tijms

### Chapter 2: Law of Large Numbers and Simulation

1. LLN for probabilities
2. Basic probability concepts -(Sample Spaces with Equally Likely Outcomes)
3. Expected Value and the LLN

### Chapter 4: Rare events and lotteries

1. Binomial distribution
2. Poisson distribution
3. Hypergeometric distribution

### Chapter 7: Foundations of Probability Theory

1. Probabilistic Foundations
2. Compound chance experiments
3. Basic Rules from axioms

### Chapter 8: Conditional Probability and Bayes

1. Conditional Probability
2. Law of Conditional Probability
3. Independence of events

### Chapter 6: Chances trees and Bayes’ rule

1. Monty Hall dilemma

### Chapter 9: Basic rules for discrete random variables

1. Random Variables and Expected Value (review)
2. Expected value of sums and Substitution rule
3. Variance, Standard Deviation and Chebyshev’s Inequality
4. Independence

### Chapter 10: Continuous Random Variables

1. Concept of density
2. Expected value

### Chapter 5: Probability and Statistics

1. Histogram
2. Normal Curve
3. Central Limit Theorem
4. Graphical Illustration of CLT
5. Statistical applications
6. Confidence intervals for simulations