Rodrigo Ribeiro, Ph.D.
Professor
IMPA Tech
Sala 02
Intro. Probability and Statistics [Summer Course]
July 1, 2022 August 1, 2022
University of Colorado Boulder
Undergraduate
Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing.
Chapter 2: Law of Large Numbers and Simulation
- LLN for probabilities
- Basic probability concepts -(Sample Spaces with Equally Likely Outcomes)
- Expected Value and the LLN
Chapter 4: Rare events and lotteries
- Binomial distribution
- Poisson distribution
- Hypergeometric distribution
Chapter 7: Foundations of Probability Theory
- Probabilistic Foundations
- Compound chance experiments
- Basic Rules from axioms
Chapter 8: Conditional Probability and Bayes
- Conditional Probability
- Law of Conditional Probability
- Independence of events
Chapter 6: Chances trees and Bayes’ rule
- Monty Hall dilemma
- Test Paradox
Chapter 9: Basic rules for discrete random variables
- Random Variables and Expected Value (review)
- Expected value of sums and Substitution rule
- Variance, Standard Deviation and Chebyshev’s Inequality
- Independence
Chapter 10: Continuous Random Variables
- Concept of density
- Expected value
Chapter 5: Probability and Statistics
- Histogram
- Normal Curve
- Central Limit Theorem
- Graphical Illustration of CLT
- Statistical applications
- Confidence intervals for simulations