Syllabus MATH 3510

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
2. Test Paradox

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